Cahill, 25, is out of contract in the summer and has attracted the interest of several Premier League sides, and both Arsenal and Tottenham made a bid to sign him during the summer.
Asked if he expected Arsenal to return for the player, Coyle said: "I wouldn't be surprised. Arsene's always said he's a big admirer of Gary Cahill and ultimately the clubs never reached a fee - certainly the two chairman never got to a fee they felt was agreeable.
"Gary's got nothing to prove. Gary's an outstanding player and an outstanding young man, but I do think come January there'll be more than Arsenal come calling for Gary. For the moment he's got to focus on doing his job for Bolton Wanderers, which has elevated him to the England team.
"Obviously that's January's problem. He has has to make sure he's focused on that, and he will because he's very conscientious and he's a lovely young man."
Coyle had said last month that "the word derisory doesn't even cover" Arsenal's previous bid for Cahill but, ahead of Bolton's trip to the Emirates on Saturday, he dismissed suggestions of a feud between the pair.
"I am a huge admirer of Arsene Wenger," Coyle said. "I have come up against him many times and there will be no tension."
On the recent criticism of Wenger, he added: "It is absolutely ridiculous. Arsene Wenger is one of the best managers in world football, and always will be, but we have to accept football is a game of opinions and criticism comes along the way.
"I feel he is the perfect fit for Arsenal though, given their history and tradition and the way they have evolved over the years. Yes, they would like a trophy, but look at the players he has brought to the club.
"Maybe if he had the same resources as other managers of the biggest clubs, you would see an Arsenal side with different personnel."
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