The Emirates Stadium supremo has revealed that he is not interested in signing the France international, insisting that he has enough midfielders at the club - although whether he includes captain Cesc Fabregas in that list remains to be seen.
Fabregas remains widely expected to return to former club Barcelona before the start of the new season, although the Catalans appear to be struggling to raise enough money to fund the deal - with Arsenal thought to have already turned down a £30 million bid.
The Arsenal skipper is currently in his homeland, having returned with the rest of the triumphant Spain squad from the World Cup in South Africa.
He was the subject of a prank from Barca duo Carles Puyol and Gerard Pique on Monday night, with the Catalan pair forcing a Barcelona shirt over his head in front of the mass gathering of Spanish fans celebrating in Madrid.
With Fabregas expected to leave, Wenger has been linked with a string of potential replacements including Germany maestro Mesut Ozil and Gourcuff, who would team up with former Bordeaux team-mate Maroaune Chamakh were he to join the Emirates Stadium outfit.
However, the Gunners' boss has revealed that he has no plans to sign the France midfielder - sent off in his country's final World Cup match against South Africa - last month.
“We are not interested and we have never contacted Bordeaux,” Wenger told Eurosport.
“He's a player I like a lot, but we are sufficiently covered in midfield.”
