The Gunners are due to play in the FA Cup fourth-round tie against Blackburn on Saturday and the north London club has yet to announce whether Wilshere will play a part.
Wilshere will be closely monitored after coming off against Sunderland last week with a dead leg, just days after his heroic display for England in the win over Brazil at Wembley.
Wenger started Wilshere on the bench for the last FA Cup tie at Brighton, where his second-half introduction helped spark a late rally to secure a 3-2 win.
However, the Gunners boss knows just how crucially a fully-fit Wilshere will be for his side's hopes to progress in Europe, and so could err on the side of caution if the midfielder is touch and go for on Saturday.
"Jack is looking better, but is still a doubt. He got a kick on the thigh," the Arsenal manager said.
Wenger is likely to try to protect the fitness of several key men, while also seeing off the challenge of Blackburn who were thumped 7-1 on the last visit 12 months ago as they headed for relegation.
Captain Thomas Vermaelen missed both the last two matches because of an ankle problem, which has been requiring injections.
The Belgian centre-half said during a Q&A with fans on Arsenal's official Twitter account yesterday: "At the moment I feel great, I trained all week, so hopefully I will be back really quickly."
Centre-half Laurent Koscielny is another doubt with the calf injury which saw him limp out of the warm-up last weekend, after originally picking up the problem while away on international duty with France.
Full-back Carl Jenkinson will be suspended for the cup tie after his red card for two cautions at Sunderland.
With Kieran Gibbs still sidelined by a thigh problem and Andre Santos having joined Brazilian side Gremio on loan, Wenger's defensive options are stretched, so Ignasi Miquel, the 20-year-old Spaniard, looks set to be involved again this weekend.
Centre-back Per Mertesacker maintains Arsenal must put all thought of tackling Bayern Munich out of their minds as they look to book safe passage into the quarter-finals of the FA Cup.
"We still have an important cup game on Saturday (first) - we absolutely want to advance in the FA Cup, that is why the preparations for Bayern are not that intense yet," the Germany international said.
"However, beginning on Sunday the preparations for Tuesday's match will be extreme."
Saturday sees the start of a crucial period which could well define Arsenal's season, as they go to Tottenham on March 9 and then host Everton before travelling to the Allianz Arena for the second leg.
Mertesacker added: "Bayern are doing superb this year and that is a big challenge for us, but we are looking forward to both legs."