Hoops manager Neil Lennon has made Baldock one of his top targets in the search for a new right-back.
Lennon has lost three options in the position already this summer. Jeremy Toljan has returned to Borussia Dortmund after his loan, while Cristian Gamboa has been released.
The club has also failed to agree a new deal with Mikael Lustig and he is expected to return to Sweden as a free agent.
That is why Lennon has turned to Baldock and despite the Blades’ promotion, the 26-year-old wants to speak to the Scottish champions.
Chris Wilder does not want to sell the full-back, but he is about to enter the final year of his current contract at Bramall Lane.
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However, apparently Wilder is prepared to lose Baldock on a free transfer in a year’s time rather than selling him this summer.
Which is perhaps why the Bhoys have turned to other options. It seems that both Arsenal’s Carl Jenkinson and Adam Matthews are being considered. Matthews is a former Celtic player and has just been released by Sunderland.

What if Baldock joins Celtic?
The same Express article says that it would cost around £3m to sign Baldock. Other reports also claim that the Blades are looking at options in his position.
The Daily Mail says a contract has been offered to Antonio Valencia. The 33-year-old is on the search for a new club having left Manchester United after 10 years.
A move to MLS appears to be more likely, though.
Meanwhile, another free agent – Todd Kane – is being linked by Football Insider. Kane has left Chelsea and Aston Villa, Derby County and Fulham are also thought to be interested.