Manchester City are believed to be keen to offload Wright-Phillips and the England winger has been linked with a move to Fulham, as well as the Trotters.
However, it is reported Bolton are unwilling to add the midfielder to their wage budget and Coyle has suggested he is not interested in signing Wright-Phillips.
"We can sit here and a million names can be bandied about," Coyle said. "But the bottom line is that there is nothing positive or concrete to report on players. It's pure speculation."
However, Bolton do appear to be closing in on Wheater, who is out of contract at the end of the current season. Championship side Middlesbrough have confirmed they expect the 23-year-old to leave the club.
"In an ideal world he gets sold," manager Tony Mowbray said. "It seems a strange thing to say but otherwise he will walk away for nothing in the summer."