The 26-year-old Derby defender is wanted by Ligue 1 side Marseille, the club where he spent last season on loan, and they have lodged a £1.3million bid.
However, Burnley have also had an offer accepted and Coyle is optimistic he will get his man, especially as Mears has a desire to remain in England and returned early from holiday to begin discussions.
"Tyrone was in Marbella but, to be fair to the lad, such was his keenness, he was prepared to fly in from there," said Coyle.
"Marseille wanted to make the move permanent, so there's no doubt about the level he's capable of playing at.
"He's 26, been in the Premier League and he's moved for over £1million twice, so it shows you the value people place upon him.
"I've liked him for a number of years, but equally I would think he's got a point to prove. He wants to show he's a Premier League player.
"He's had a taste of that. I would hope, and I've got no doubt having spoken to him on the phone, he's keen to do ever so well as a Premier League player."
Coyle believes Mears, who has a year remaining on his Derby contract, will fit in well at Turf Moor.
"If he can fit in under our umbrella then it would be a tremendous acquisition for the club, because he's got pace and power, he's hungry and he wants to show people he can play at that level," the manager told the Lancashire Telegraph.
"He's not someone who is coming here for a pay day; he's coming here to show what he can do and aspire to be even better, and that's the type of player that I love working with."