HITC Sport understands Sheffield Wednesday ace is in their sights.
Tom Lees of Sheffield Wednesday
Leicester are set to return with an improved offer whilst Everton have also been linked for Keane, and Burnley boss Sean Dyche is already looking at potential replacements.
Tom Lees - Sheffield Wednesday
Top of his list is Lees, who has been outstanding for Wednesday since joining them from Leeds United in 2014 and he penned a new four-year deal with The Owls last summer.
But now having failed to achieve promotion themselves, the South Yorkshire club know they face a battle to hang onto 25-year-old Lees.
It is understood that even if Keane remains at Burnley, Dyche wants the club to push ahead with a move for Lees. They have also been linked with a move for Grant Hanley from arch-rivals Blackburn.