Wenger wants the 25-year-old Holland international - who joined the Gunners in May 2004 - to play his part in Arsenal's future.
"I am hoping he will sign a new deal and I am trying very hard to get him to sign. I want Robin on board," said Wenger. "He is a very important player in the squad and on the pitch he is a very efficient player."
Wenger added: "We want him to stay because we gave him a chance when he was in a very bad position at Feyenoord.
"I think he developed well here and I don't see a reason for him to go and he loves the club. We will let you know as soon as we get close."
Wenger maintains the club must do all they can to keep the players they have nurtured.
"You cannot imagine that we work as we did with young players and give them a chance, then let them go," he said.
"We are criticised because we play young players, then we are supposed to let them go when they are in a position where they start to perform at the top level? That is not acceptable."