But Wenger insists Becks is welcome back to train with the Gunners, like he did during the previous MLS close season.
Becks is close to agreing a deal with AC Milan that will see him join the Italian side on loan in January.
He said: “I have not been in touch with him and certainly not as a player for the club.
“But if he wants to be fit and practise, why not?
“However, we have Theo Walcott who plays in this position and Emmanuel Eboue who plays in this position, so we are not looking for a right midfielder.”