The Latics manager his emphasised that he wishes to see James McCarthy remain at the club and urged Ireland boss Trapattoni to allow him to do his job at Wigan
The Republic of Ireland boss suggested that McCarthy, who joined Wigan in 2009, needed to seek a transfer away from the Championship club in order to fulfill his potential.
Indeed, recent reports indicated that Premier League clubs such as Liverpool, Everton, Tottenham and Fulham had expressed interest in the player, with Wigan placing a £20 million (€23 million) price-tag on his head.
However, Coyle, who was recently appointed as the successor to Roberto Martinez, stressed that the club did not wish to sell the 22-year-old midfielder.
"If that's what Mr Trapattoni thinks, I could say to him that he [McCarthy] should be starting every game for Ireland," Coyle told the Irish Examiner. "He's got his job to do with Ireland and let respective football managers do their jobs at their clubs. That's what I'd say to Mr Trapattoni."
Nevertheless, Coyle conceded that it was "part and parcel" of football to have big clubs expressing interest in talented players such as the Ireland international.
He continued: "We don't, as a football club, want to sell anybody or have to sell anybody, but we understand how football works and when you have got very talented players there will always be interest.
"That just goes part and parcel with the game."