Blues boss Andre Villas-Boas revealed on Friday the parties were "miles apart" in their negotiations over personal terms after a £7million fee was agreed with Wanderers.
Villas-Boas would not go into details about the impasse with Cahill - although one issue is understood to be the player's salary - or whether Chelsea had made a take-it-or-leave-it offer.
The Portuguese was nevertheless hopeful of a positive outcome, saying: "I think we can sort it out - it should be no problem.
"It's in my chief executive's hands at the moment. It's an ongoing conversation.
"We'll have to wait for the best outcome. The best outcome for us is for the player to join us."
However, Villas-Boas warned Chelsea would turn elsewhere if an agreement could not be reached.
"We will continue to monitor this situation as we continue to monitor the other targets for this position," he said.
England star Cahill is not short of admirers, with Arsenal seeing a bid rejected for him in the summer and Tottenham also coming close to landing the defender.
Spurs retain an interest and may choose to gazump Chelsea, as they did when signing Steven Pienaar from Everton in January.
Villas-Boas had no doubt about Cahill's qualities, despite Bolton's current struggles in the Premier League.
He said: "I think his technical attributes are immense. His pace is fantastic as well.
"There are weaknesses. But they're also related to the collective organisation of Bolton.
"He's a player who has been playing magnificently well at international level, normally alongside John Terry, and he can add to this squad or any squad in the Premier League. He can make this jump."
Bolton boss Owen Coyle was confident Cahill would give his all in what could be his final game for the club against Wolves.
He said: "I have said to Gary that he has to be focused on giving everything for Bolton Wanderers, because he knows Bolton Wanderers has been terrific for him just as much as Gary has been for us.
"That is why they have representatives - to sort that out - and whatever January 1 brings, it will bring."
An early January sale of Cahill, who is out of contract in the summer, would give Coyle plenty of time to buy a replacement.
New York Red Bulls defender Tim Ream has been linked, as has Chelsea midfielder Josh McEachran on a loan deal.
Villas-Boas reiterated yesterday Bolton would not receive preferential treatment should Cahill complete his move in the opposite direction.
But the Chelsea boss did confirm he was considering farming out McEachran, who is also wanted by Premier League new boys Swansea.