Wenger said the Gunners had not discussed any extension with the Red Bulls but acknowledged it was possible.
"I haven't looked at it," Wenger said Saturday. "Maybe the maximum possibility we have is two more weeks."
That would make the 34-year-old striker available for an FA Cup match and what could be a crucial Feb. 26 meeting with local rival Tottenham.
Henry scored in injury time to round off the rout, a match that is currently scheduled to be the former France star's last in front of the home fans at Emirates Stadium.
The goal extended Henry's club-record haul to 228 — 226 in his first spell from 1999-2007 and two more since returning on loan from MLS.
Wenger said Henry had lifted the club since returning.
"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," Wenger 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."