Club policy at Arsenal is that players over 30 are only offered one-year contract extensions but Wenger was somewhat vague when quizzed about Gallas.
Conceding an exception could be made due to the player's position, Wenger appears determined to keep Gallas, being of the opinion his experience is key in what is a young squad.
"One year? Unfortunately that is the rule here, except for the manager," he said.
"For a striker after 32 you can only give a year contract. For a centre-back you can be a bit more comprehensive with the situation. We'll see.
"William has been amazing the whole season. He does what you dream of as a manager - he does not talk and plays well. What you respect is how well he responded when he was not captain any more.
"At some stage I considered Gallas might leave, but he's learned that being appreciated is important. The young players respect him. It is always the same in life: if you have the right attitude then people will rate you.
"He had the right attitude, that means he has maybe found appetite again for the club."
Source: Team Talk
Source: Team Talk