With Thomas Vermaelen and Sebastien Squillaci currently consigned to the treatment room, Arsenal are keen to bolster their back line with a January signing, and Cahill is believed to fit the bill.
The Trotters' acquisition of David Wheater from Middlesbrough this week has indicated that Owen Coyle's side are preparing for the departure of Cahill, but Wenger is keeping his cards close to his chest in terms of the Gunners' transfer activity.
"At the moment, I cannot come out with any name," he said. "I think Gary Cahill is a very good player, but I cannot tell you more.
"We like to keep our transfer negotiations always very secret, because it puts more pressure on when you go public so you would understand we don't want to speak publicly about that."
Emirates Stadium supremo Wenger admits he would like to bring in a new central defender this month. However, the Frenchman is confident that he already has the players to cope with the current injury crisis if a new recruit is not forthcoming.
"It is a worry as long as [Sebastien] Squillaci is out, I must say, as we are short, but we have other resources," he said.
"If the worst came to the worst, [Abou] Diaby is coming back so if we have to put [Alex] Song back we have Diaby coming back to play in midfield."
Cahill has played 96 times for Bolton since arriving from Aston Villa, winning one cap for England in a European Championships qualifier against Bulgaria in September 2010.
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