The 39-year-old Frenchman enjoyed a successful six-year spell with the Gunners before leaving for Villarreal in 2006.
When asked if Pires would be offered a contract, Wenger told reporters: "No, Robert Pires will not join us, he was born in 1973.
"He is still very fit and a great player and we are always happy to have him in training but he just occasionally comes in to practice.
"He practises with the young players with the Under-21 team, and I feel always there is no better education than playing players at that age with top-level players."
Arsenal return to action on Tuesday when they welcome Serie A side Napoli to the Emirates Stadium in the Champions League.