The 25-year-old is entering the final year of his contract and Gunners boss Arsene Wenger has been consistently linked with the England international.
Wenger is keen to bolster his defensive options and has money available following the departures of Cesc Fabregas and Samir Nasri.
But Bolton boss Owen Coyle says the two clubs are a distance apart in terms of their valuation of Cahill.
He said: “It is nowhere near our valuation as a football club of Gary Cahill.
“I had a chat with Gary prior to the Macclesfield game to explain what had taken place.
“Gary’s representatives had been made aware there had been a so-called offer, but given the amount that was talked about I don’t call that an offer.
“If I make an offer for someone I do it in writing so you know exactly where you are with it. It is fair to say the dialogue was nowhere near what the football club would even consider for Gary Cahill to leave Bolton Wanderers.”
The offer has been reported at being £6 million and Bolton chairman Phil Gartside re-tweeted a message by a Wanderers fan angered by the bid.
But Wenger was himself angered by Bolton’s reaction and insisted that figure was not correct.
Coyle had said earlier in the summer that he was resigned to losing Cahill, but that he would only sell him if the right offer came in.
While the former Republic of Ireland international believes the defender would fit in well at Arsenal, he has reiterated that he will not sell on the cheap.
“I am very respectful of Gary’s wishes in this as well,” he said. “I totally understand he wants to play at the highest level and Arsenal are an elite club, a club I think he would probably slot in to with tremendous style because he is such an accomplished player.”
He added: “But it has to be done at the right business for Bolton Wanderers Football Club.
“It was way, way short and I must stress the word way as it was a million miles short of what Gary Cahill’s valuation is.”
While Coyle may yet lose the defender before the transfer window closes on Wednesday, he has strengthened his back line with the signing of Dedryck Boyata on a season-long loan from Manchester City, although the Belgium international is not available for the trip to Merseyside.