The 35-year old midfielder trained with the Gunners two years ago when the Major League Soccer had its off-season and Wenger says he would love to have him back at the Emirates.
But he also stressed that now is not a good time for his side to bring in a midfielder.
“I love David Beckham and when he was here he was a fantastic example on the professional side. He was the first in and the last out,” Wenger said.
“It’s in an area where we do not need players. We have Theo Walcott, Samir Nasri, Tomas Rosicky, Andrey Arshavin, Carlos Vela, Emmanuel Eboue who can play on the flanks. I cannot sign anybody in January in the department where he plays.”