The 26-year-old enters into the final year of his contract and the Hoops are keen on bringing him to Scotland.
Baldock,26, has been exceptional for the Blades this season and played a huge role for his side to earn promotion after a decade. He appeared for 27 games with a goal tally of three in all competitions.
However, the English full-back is willing to seek an exit despite the fact he will play in the Premier League next season.
Having progressed through the youth ranks of Milton Key Dons, Baldock struggled at the start to get enough playing time as he spent subsequent loan spells with various clubs. But he soon became a staple of the club in the latter half of his spell, eventually making 125 appearances.
Celtic’s right-back conundrum
The Hoops are contemplating a lot over the position of right-back with Mikael Lustig’s future at Celtic Park remaining unclear.
The Swedish international is already in the twilight of his career and has got an interesting offer from his country-bound club Malmo.
Read more Celtic FC News, click here – Latest Celtic FC News
And Neil Lennon is in need of a quality full-back, who could be as good as Lustig in his stead. Baldock has the tendency but his stats in terms of attacking are a little worrying. In addition, he lacks experience in Scottish football and it remains to be seen whether he could adapt to the club’s playing style.