The 35 year old former England defender has been training at the Gunners' Hertfordshire base since leaving Notts County.
Wenger said: "I do not know yet, I have not really thought about that.
"At the moment, we have four centre-backs and we will always have four.
"If one would go, then I would consider it, but at the moment we are four, so I have no need to sign anybody else."
Wenger added: "I love Sol Campbell and the fact he came back here and wanted to practice with us shows he loves the club as well.
"You never say never in these kinds of situations."
The Gunners boss insisted Campbell could still cut it at the highest level.
"Sol can still do a job in the Premier League, especially now he is fit. He has worked very hard," Wenger said.