Henry is regarded as one of the greatest players to have ever pulled on an Arsenal shirt, winning two league titles and three FA Cups during a hugely successful eight-year spell at the club.
The Frenchman, who is the club's record all-time scorer, left Arsenal in 2007 for Barcelona before moving to the United States where he currently plays for the New York Bulls.
The 34-year-old has been training with the Londoners since the close of the MLS season in November and recently had a statue of him unveiled at the Emirates Stadium to underline his legendary status at the club.
Henry will not be required back in the United States until March and Wenger will lose Gervinho and Marouane Chamakh for up to a month at the end of January due to the African Nations Cup, leaving him short of strikers.
For that reason, Wenger is considering the possibility of a potential two-month loan deal for the star.
"I have to think about that," Wenger said. "Short term is ideal for us, but I haven't made any enquiry yet. Thierry is not here at the moment. It has never come up in conversation.
"January 1 is the vital date for us. We have seven days to make decisions and I will make a decision in the next seven days on players."
Robin van Persie equalled Henry's club record of 34 league goals in a calendar year at Aston Villa on Wednesday as the Gunners returned to winning ways with victory over Alex McLeish's side.
The Dutchman now has two more games to see if he can pass Alan Shearer's Premier League record of 36 goals in a year, which was set in 1995.
Wolves and QPR are Arsenal's next two opponents, and in his current form few would bet against the 28-year-old reaching his target.
Wenger, however, played down the significance of the record, arguing that six more points are more important than personal accolades.
"The individual records are not vital for me, they are just a sign that the team scores," Wenger said.
"He is an exceptional player, but what is important is that we win our games this Christmas."
Wenger's team host Wolves on Tuesday after having the fixture put back 24 hours due to a tube strike in the capital.
The Gunners boss, already shorn of four of his first-team defenders, announced yet more bad news from the treatment room.
Wenger confirmed that Kieran Gibbs will be out for a month after having to undergo surgery for the second time this season on his troublesome stomach injury.
The 22-year-old's latest setback is bad timing for Wenger, who is already without full-backs Andre Santos, Bacary Sagna and backup defenders Johan Djourou and Carl Jenkinson.
Gibbs' injury means Arsenal are likely to delve in to the loan market, but Wenger denied reports he has already lined up a move for Manchester City's out-of-favour full-back Wayne Bridge.
"I haven't made any inquiry yet for Wayne Bridge or anyone else," Wenger said.
"It is of course something we will look at but it depends on how long you have to take them.
"I have to see what is available - if I have a good opportunity then why not? They have a big impact on your wages.
"If you have to sign a player for three or four years and then you have three or four left-backs, only one can play, so they are not happy.
"It can only be a short-term solution for us because we have bought Santos, we have Gibbs, we have Vermaelen who can play there (left-back), so we do not need a long-term solution."
Wenger still thinks youngster Gibbs, who was called up for the England squad earlier this season, can make Fabio Capello's Euro 2012 squad despite the injury.
"He is incredibly unlucky, but he still can play in the Euros, because they are in June and we are in December," Wenger said.
"Normally this injury would keep him out for four weeks, so there is still a good opportunity."
Top 10 Henry Goals for Arsenal
Real Madrid 0-1 Arsenal (21/02/06)
It was fitting that in the grandiose arena of the Bernabeu Henry produced one of his finest goals in an Arsenal shirt. After receiving the ball in the centre circle, Henry breezed past four Real Madrid players before producing a cool left-footed finish past Iker Casillas to give Arsenal a 1-0 first-leg victory.
Sparta Prague 0-2 Arsenal (18/10/05)
Henry equalled Ian Wright's Arsenal goalscoring record of 185 goals with a superb effort against Sparta Prague. After showing superb control to bring the ball down on the edge of the area, Henry sent a magnificent curling half-volley with the outside of his right foot past the helpless Sparta keeper.
Arsenal 4-0 Charlton (02/10/04)
With Arsenal 1-0 up at the start of the second half, Henry produced yet another bit of magic. Receiving a pass on the edge of the six-yard box with his back to goal, the Frenchman shielded the ball before producing a magnificent back flick into the far corner.
Arsenal 4-2 Liverpool (09/04/04)
Having been beaten in the FA Cup semi-finals and Champions League quarter-finals in the same week, Arsenal were in danger of slipping against Liverpool. With the game finely poised at 2-2, Henry picked the ball up just inside the Liverpool half and breezed past Dietmar Hamann and ghosted past Jamie Carragher before sliding the ball beyond Jerzy Dudek.
Arsenal 1-1 Man United (28/03/04)
Arsenal were looking to kill off Manchester United's title challenge at Highbury and once again it was Henry who produced a spectacular strike. Following good work by Reyes, Henry took the ball 35 yards out and fired a powerful swerving strike past Roy Carroll.
Inter Milan 1-5 Arsenal (25/11/03)
Arsenal needed a win in the San Siro in a crucial Champions League group game. And it was Henry once more who was their inspiration on one of the Gunners' greatest European nights. With the score finely poised at 2-1 with five minutes remaining, Arsenal broke and the ball came to Henry in his own half. The Frenchman set off on one of his trademark sprints into the box and teased one of the world's best defenders, Javier Zanetti, before firing an angled left-foot drive across Francesco Toldo.
Arsenal 3-0 Tottenham (16/11/02)
Arguably his greatest goal in an Arsenal shirt and a particular favourite among Gunners fans, Henry scored a quite magnificent solo effort against north London rivals Spurs. After a Tottenham throw had been headed clear of the Arsenal area, Henry controlled the ball deep inside his own half before sprinting to the other end, dummying past two Spurs defenders and smashing a low left-foot shot past Kasey Keller.
West Ham 2-2 Arsenal (24/08/02)
Arsenal were 2-0 down at Upton Park before Henry brought them back into the game in spectacular fashion. Patrick Vieira passed to Henry some 40 yards from goal and the Frenchman flicked the ball around a West Ham defender, brought it down with his chest and struck a vicious half-volley into the top left-hand corner.
Arsenal 1-0 Man United (01/10/00)
Possibly the goal which really announced Henry's arrival in the Premier League. Receiving the ball on the edge of the area, with his back to goal and being closely marked by Denis Irwin, Henry flicked the ball up with his right foot and in the same movement turned and sent a spectacular volley over Fabian Barthez.
Southampton 0-1 Arsenal (18/09/99)
With a £10.5million price tag and no goals after his first eight Arsenal games, Henry was under pressure to deliver. And deliver he did, taking a pass from Arsenal captain Tony Adams, cutting inside on to his right foot and curling a delightful effort from 25 yards for his first Arsenal goal.