The 28-year-old defender has been linked with a move away from Sampdoria during the winter transfer window and several clubs are chasing him.
Celtic have been linked with holding an interest in taking Colley to Scotland and are considering adding him to their squad to solve their defensive woes in January.
Fenerbahce are also chasing the 28-year-old centre-back, but it has been claimed their chief rivals for his signature are from the Premier League.
Sheffield United have been keeping tabs on Colley for months and the club are now serious contenders to sign the defender.
Chris Wilder’s side have earned just a point from their opening 14 league games and are already being tipped to go down.
The Sheffield United manager wants to bring in a centre-back in the winter window to solve some of their defensive problems.
And Colley has emerged as one of the top targets for the club as they look to strengthen their squad.
Sheffield United are likely to want Colley on loan with an option to buy if they stay up.