Nasri, 23, and Clichy, 25, remain a key part of the Arsenal first-team and it would be a major blow if they decided not to prolong their stay at Emirates Stadium, but Wenger says he is "very optimistic" they will pen extensions to their current deals.
"We are talking to Nasri and his agent already and we have the same situation with Clichy," he said. "We have agreed to speak about it during the summer."
There have been suggestions that the likes of Cesc Fabregas are growing increasingly frustrated with the failure to win silverware, but Wenger has stressed that the players must take responsibility for success on the field.
"The players have the opportunity here to do it in their own way, with their own philosophy, with their own togetherness," Wenger said. "When you sign a contract for four or five years, you are committed through your contract to win trophies with the club where you sign.
"It is in no contract that if you do not win a trophy the first year, you can leave."
He added: "Nobody asks them to wait. We can win straight away. You speak like the players are not responsible for winning trophies. They are as well responsible, as I am, as the fans are.
"Why do you think we pay the players? A club, a football team, is a togetherness between the manager, the players, the club, the philosophy, and a commitment.
"After that you can have some individual situations, but it cannot be a philosophy that if at any time we do not win I should move on. It is down to belief, the direct consequence of the motivation you put into your next game.
"If your belief is very low, your feeling is very low. What I think we can get from our performances is the belief that we have the quality."
Arsenal need to beat Bolton on Sunday if they are to retain any hope of overtaking Manchester United, but many believe the failure to beat Tottenham in midweek has already ended their chances.
Wenger has been criticised for his failure to add experienced campaigners to the squad and, although he said this week that he feels "there is always a need to improve the team" and that the Gunners "can make a big transfer" if needed, he does not want such talk to detract from their aims this season.
"We are fighting for the championship and I am always sitting in a position where you force me to explain why we fail," Wenger said. "For me it's not a comfortable situation because we are fighting in a period where the most important thing is to have belief in what we do and you keep saying, 'Why have you failed to win?'.
"Let's just play for it first and have a go. For me it is important to give absolutely everything until the last game of the season, to be proud, and then, as I have said many times, if there has been somebody better we will have to accept that.
"But at the moment I don't accept that there is somebody better."