Ange Postecoglou, the Parkhead boss, has identified Baldock as a possible new acquisition after succeeding Neil Lennon as boss of the Hoops.
And Gabby Agbonlahor, the former Aston Villa striker turned pundit, believes it would be good move for the “passionate” right-back.
Speaking to Football Insider, he said: “I’ve really liked him at Sheffield United since they came into the Premier League. He looks so calm on the ball with his passing, he’s energetic going forwards and backwards.
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“He’s passionate so he suits the Scottish league and a big club like Celtic.
“For me, that’s something that I’d definitely try and get it done and over the line.”
Celtic, though, have not yet made contact with United over Baldock, who signed a new four-year deal at United in 2020.