Cahill caught the eye at the heart of Bolton's defence last season, attracting the attention of numerous Premier League clubs. Potential suitors have included Arsenal, but, as yet, no formal approach has been made for the England international.
Fresh reports have suggested the 25-year-old is being lined up for a big-money switch to Anfield - claims that Coyle feels are derisory.
"This story is without a shred of foundation," he said. "It is irresponsible. To just reel words off is in poor taste. Nothing surprises you in football but people should have more knowledge of the background for anything before they write it.
\"It doesn't faze me. I am not raging about it. I am just making a point."
The current transfer window closes on August 31 and Coyle is adamant he will not concern himself with "hypothetical" developments.
"There are 27 days left," he said. "This is another one. Nothing has happened, there is nothing concrete, there is nothing to report. If someone leaves, it will be the right business for the club but I don't pre-occupy myself with thoughts like that when I have a team to prepare for the rest of the season.
"If anything happens, we will re-adjust. At the moment it is hypothetical, so will focus on the players we want to add to the club. Gary had been through that much and read so many things, he is really focused. That is the way we will treat it. It is not difficult for me either because there is nothing to chat about."