The centre-back has been the subject of long-term interest from the Gunners, but Trotters boss Owen Coyle has slammed the offer, insisting it "wasn't even close" to their valuation
The centre-back has only a year remaining on his contract with the Trotters and Coyle has maintained throughout the summer that the England international will be allowed to leave for the right price.
Arsenal are looking to delve into the transfer market to spend the money received for Samir Nasri and Cesc Fabregas this summer and a partner for vice-captain Thomas Vermaelen is among the club's top priorities.
However, Coyle has now revealed that the Gunners' offer, which is believed to be in the region of £6 million, falls way short of Bolton's valuation.
He said at a press conference: "There was a conversation between [chairman] Phil Gartside and a representative of Arsenal. I'm only passing this on as a third party, but the word 'derisory' doesn't even cover it.
"When I make an offer for a player, I'd like to think in the right ball park, but this wasn't even close.
"I spoke to Gary Cahill about it before the Macclesfield game, and he knows everything that's going on."
Cahill signed for Bolton in 2008 for £5m from Aston Villa and has since won plaudits and three England caps for his assured displays at the heart of Wanderers' defence.