Bolton rejected an offer from Arsenal for Cahill earlier this week, with Coyle labelling the bid 'derisory' and insisting he is under no pressure to sell the defender, despite his contract being up at the end of this season.
The Gunners are expected to return with an improved offer this week, with £12 million likely to be enough to prise Cahill from the Reebok Stadium.
But Coyle insists he will only accept top dollar for the England international, who he understands may wish to move on to further his career.
"Everybody knows Gary's desire to play for an elite club, with the Champions League and everything else," Coyle said. "I fully endorse that but he is an outstanding man as well as a footballer. I've had a chat with Gary about it and he knows my opinion.
"The bottom line is, we don't have to be taking poor offers. I would probably want more for Gary than would be accepted but it still has to be a good offer. I think Gary could play for anybody, so my valuation would be higher than anybody's."
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