Defender George Baldock, who has been a first-team regular at Bramall Lane since joining from MK Dons in 2017, is understood to be a target for Scottish giants Celtic.
The 28-year-old was previously of interest to the Hoops in 2019 when Sheffield United were promoted to the Premier League.
Elsewhere, Sander Berge continues to be linked with a move away from the club, with another Premier League giant reportedly quoted a bargain price.
United begin their pre-season training today with the players meeting up a few days before new boss Slavisa Jokanovic officially takes charge on Thursday.
He is expected to be speaking to those linked with moves away as a matter of priority when he arrives in Sheffield.
Here are the latest transfer rumours from Bramall Lane and around the Championship.