Mark Hughes is still desperate to land a big-name defender before the start of the Premier League season, and switched attention to Toure once his high-profile move for Chelsea captain John Terry collapsed.
The 28-year-old could now fly back from Arsenal's pre-season tour of Austria to discuss terms and have a medical.
Wenger said the next 24 hours were potentially decisive. He told Arsenal TV: "We will see what's happening in the next 24 hours, nothing is decided yet.
"We have seven centre-backs and I am in the position where I have to play some in midfield but of course Kolo is a very good player and we will see what will happen in the next 24 hours."
Toure has spent seven years at Arsenal and is the only remaining member of Wenger's squad to have played regularly in the Invincibles campaign of 2003-04.
The 28-year-old had an inconsistent season and was dropped several times by his manager. And with a bumper fee on offer for Wenger and huge wages in prospect for Toure, both parties could be willing to do a deal.
Arsenal have strengthened their back line this summer with the £10m capture of Thomas Vermaelen from Ajax, and Wenger revealed there could be more new faces in before the new season gets underway.
He said: "I am more focused on getting everybody fit for the start of the season but we are looking at opportunities as well, there are still some pre-season games to see what we really need. When the time comes we will do something.''