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.
1. Southampton hunt Blackburn striker
Adam Armstrong of Blackburn Rovers is on Southampton's radar, The Athletic report. The forwards was one of Rovers key men last season and with Danny Ings expected to leave St Mary's the Saints need to replace his goals Photo: Jan Kruger
2. Brentford set to sign Nottingham Forest defender
Top flight newcomers Brentford are set to sign defender Joe Worrall from Nottingham Forest, according to The Sun. The Bees are looking to add depth to their squad ahead of their first Premier League campaign. Photo: Nathan Stirk
3. Rumoured Blades target seals move elsewhere
Jack Hendry, who has been linked with Sheffield United, has completed a permanent move to Oostende after a season on loan from Celtic. Photo: Petr Josek - Pool
4. Parker move could trigger Wilder approach
Scott Parker is set to leave Fulham to take over at Bournemouth, according to Sky Sports, with ex-Blades boss Chris Wilder reportedly in the frame to replace him at Craven Cottage. Photo: Marc Atkins