The Hoops have made an initial approach for Baldock and submitted an opening offer. The defender is also believed to be open to the move to Glasgow.
This is despite the fact the Blades are preparing for their first season in the Premier League in 12 years. Baldock helped them to automatic promotion from the Championship in 2018/19.
They finished second behind Norwich City, with the 26-year-old making 27 league appearances.
Manager Chris Wilder is waiting to learn his transfer budget for next season. However, he could be open to allowing Baldock to leave as he looks to improve his squad.
The full-back only has a year to left to run on his current contract at Bramall Lane.
George Baldock to Celtic is maybe a good thing
It is understood that Wilder is in the market for a new wing-back. Yet another Daily Mail article reports he wants left-sided competition for Enda Stevens.
However, Stevens – with his previous, albeit limited, top flight experience with Aston Villa – looks the more likely to make the step up.
It is on the right side of Wilder’s 3-4-1-2 formation where there are more doubts. Kieron Freeman played 22 times in the role last term as he and Baldock shared the workload.
At times it was clear that Wilder was unsure who his best option was. It would suggest that one should perhaps make way for an improved signing, with the other becoming their backup.
Currently Baldock would probably be considered first choice; but only marginally. For the Blades to compete in the Premier League they need more certainty than that.
Especially because the wing-backs play such a crucial role in Wilder’s system, providing the width and danger from the flanks.