The Gunners boss is adamant the Togo international will still be at the Emirates Stadium next season and said he does not plan any further talks.
AC Milan are pursuing the striker and Adebayor claimed on Friday he will meet Wenger next week before deciding on his future – he is demanding a pay rise to a reported £120,000 a week.
But Wenger said he already met Adebayor some time ago and has no plans to meet him again.
The Arsenal manager said: “He’s under contract and that’s quite simple. I can tell you as manager of Arsenal FC I’m not worried.
“Of course I expect him to be at Arsenal next season – he’s under contract.”
Asked if he was going to meet the striker next week, Wenger replied: “No – I’ve already met him.”
On Friday, Adebayor gave conflicting statements about his intentions. He said: “Arsenal need to tell me what they want as well. I have a promise from Arsene that they will call me next week. I’m waiting for their answer and then I’ll decide. I need to know before I come back to train on July 21. I need to know by then.”
Meanwhile, Wenger believes his midfielder Cesc Fabregas is in the running to be named player of the tournament if he thrives in Sunday’s Euro 2008 final against Germany, despite the fact the Spaniard has only started one game.
Fabregas, who is expected to replace the injured David Villa in Vienna, has however scored once and has three ‘assists’ to his name, making a big impact whenever he has come on.
Wenger, speaking at an event organised by tournament sponsors Castrol, said: “I may be biased but I would consider him as player of the tournament.
“I think Fabregas is the guy who has vision in depth, who always looks forward and those who see forward make you win – and if anybody does, it’s him.
“In the Spanish teams, he always gives them a more vertical game and makes them much more efficient when he plays.”
Wenger also believes Michael Ballack has a good chance of playing in the final despite Germany saying the Chelsea midfielder is doubtful with a calf injury.
“It’s an old Bayern Munich trick!” said the Arsenal manager. “But it would be sad if he did not play as he missed the World Cup final in 2002 because of a yellow card.
“But I’m convinced if it’s a minor injury he will play – they have very good doctors in Germany!”