Henry is due to return to New York Red Bulls after the upcoming away games against Sunderland and AC Milan on February 11 and 15 respectively but, having made a positive impression on his return, Wenger would be keen to prolong his stay.
Arsenal have an away FA Cup clash against Middlesbrough or Sunderland on February 18 and then a home league game against arch-rivals Tottenham on February 26, and Wenger said: "There is the possibility of two more weeks, but we will have to see."
Should that request be declined, Henry at least had the satisfaction of scoring the final goal in the 7-1 rout of Blackburn to bid farewell to the Emirates Stadium in style.
"With Thierry going back to the States he played, normally, his last game at the Emirates and in the last minute he scored his goal," Wenger said. "That is really something special.
"It has been very positive, everyone listens to his advice as he's delivered here and they all want to deliver. He's respected. He is still not away yet, normally until after the Milan game. Sunderland and Milan are two massive games."
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