The Ivory Coast international has reportedly handed in a transfer request after falling out of favour at the club in recent games, although it has been turned down by Arsenal chairman Peter Hill-Wood.
"I know about it (the transfer request)," Hill-Wood said. "But we are not going to accept it.
"We are not looking to let any of our players go and he is under contract - and we expect him to honour it."
The defender got into a row with former captain Gallas following the 2-2 draw at Aston Villa on Boxing Day and has now told the Emirates club that he wants to quit in January, news which will alert Manchester City who are keen on bringing the £10million-rated defender to Eastlands.
A source told the Daily Star: "Kolo doesn't want to stay - he cannot stand Gallas and Gallas cannot stand him.
"Gallas is showing him complete disrespect and Kolo believes he's been mouthing off to Wenger about them not being able to play together and Wenger is listening to him."
Toure was dropped for the unconvincing 1-0 win over Portsmouth on Sunday after playing alongside Gallas in the heartbreaking draw at Villa Park.
Despite the 27-year-old's desire to quit north London, Wenger could still reject his transfer request - but could be forced to part with the versatile defender to boost funds.
Wenger hopes to bolster his midfield ranks, with Everton playmaker Mikel Arteta and Switzerland international Gokhan Inler on the Frenchman's radar.
And with Toure contracted to the club until August 2010, Wenger could be tempted into parting with the defender to release his £3.5m-per-year salary.