Bacary Sagna, Lukas Podolski and Mesut Ozil have all been linked with moves away from the Emirates Stadium in recent weeks, but Wenger wants the squad to remain together.
Despite leading the English top flight for 17 weeks this season, Arsenal have slipped into a battle for the final UEFA Champions League qualification spot with Everton in recent months.
However, Wenger insists there are "big ambitions" at the club - who have the chance to end their nine-year trophy drought in the FA Cup final against Hull City later this month - and he believes many of his current players can play an important role moving forward.
"We want the players to stay here because this club has big ambitions for the future," the Frenchman said in a press conference on Friday.
"We want to finish as close as possible to the top and win our remaining games. European football is so close.
"One of the ingredients we've had this season was to respond when everyone was writing us off.
"We had too many injuries in March and February and we always had to play the same players.
"We missed some vital games this season but we have been remarkably consistent. Against teams who did not fight for the Premier League title we've done our job."
Arsenal face West Brom this weekend with Wenger confirming Sagna is his only injury doubt, while Kieran Gibbs and Jack Wilshere are close to a return.
