Baldock was a key member of the United side which reached the Premier League last season, after sharing the right wing-back spot with Kieron Freeman for much of the campaign.
National newspaper reports linked the Glasgow giants with a move for the 26-year-old, after Jeremy Toljan returned to parent club Borrusia Dortmund while Mikael Lustig and Cristian Gamboa prepare to leave Celtic Park.
But United are understood to be reluctant to lose Baldock, especially with the start of the Premier League season looming on the horizon, and are expected to offer him a new contract if he does remain at Bramall Lane.
His present deal, signed in 2017 after moving north from MK Dons, expires next summer.
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“It’s brilliant to have the skipper [Billy Sharp] and the manager [Chris Wilder] as the heartbeats of this club but as soon as you sign for this club, you really realise how much it means to people,” Baldock said in an interview last month.
“I live in the city and when I walk to the shops, loads of Blades come up to me and tell me how much it means to them.
“After the Ipswich game and we were all-but promoted, we went out and I had grown men speaking to me, emotional, thanking us for our efforts because of how much heartache they’d had in the past.
“I really love being part of a city that loves its football so much.”
Meanwhile, United co-owner Prince Abdullah has denied concealing WhatsApp messages on his phone from his own lawyers as the High Court battle for control of the club continued in London.