Henry's deal with the Gunners will expire on the 15th of February, meaning that the player will be available for next weekend's Premier League match against Sunderland and a Champions League encounter with AC Milan before he returns to Major League Soccer.
The Arsenal boss, however, has stated the possibility to extend the striker's loan for two more weeks.
"I haven't looked at it," Wenger told the Associated Press. "Maybe the maximum possibility we have is two more weeks."
The contract extension would put Henry up for selection in an FA Cup match on the 18th of February and a derby match against local rivals Tottenham on the 26th.
Wenger went on to mention on how the Frenchman had been a morale boost to the squad ever since his return to the Gunners.
"How much, you can never give a percentage, but he was very positive and everyone takes his advice on board because he has delivered here and they want to deliver too," the 64-year-old said. "He is respected and he was very positive."
"He is not going away yet, normally he stays until after the Milan game," he added. "So we go to Sunderland now and then we go to Milan. That is two massive games."