The highly-rated full-back is just 20 years of age, but he has already made over 120 first-team appearances for the Hoops.
His potential was spotted early by Celtic, while a senior bow when still in his teens brought him to the attention of heavyweight sides elsewhere.
Tierney has, however, grown accustomed to turning a deaf ear to transfer talk and believes the signing of fresh terms at Parkhead in October helps to highlight how his head has not been turned by talk of interest from afar.
“I’m enjoying my career here; I’ve just signed a six-year deal, so if that doesn’t say long term, I don’t know what does.”
The links to United are unlikely to go away, though, as Jose Mourinho is reported to remain in the market for a new left-back.
Tierney could be the man he turns to during the summer transfer window, with Celtic legend Chris Sutton having recently admitted that he would not be surprised to see a bid lodged from Old Trafford.
The former Hoops striker told the Daily Mail: “One thing that stands out straight away with Kieran Tierney is his personality.
“He’s level-headed, hard-working and very likeable. And he’s a grafter, someone who works hard for the team.
“It doesn’t surprise me Manchester United are after him. He’s a Jose Mourinho-type player.
“He really caught the eye in Europe last season and, amazingly, only Sporting Lisbon goalkeeper Rui Patricio has played more minutes in any top division across the world this season.
“He’s extremely solid in defence, makes good decisions and can play anywhere across the backline.
“He can improve. His final ball could be better and his attacking contribution is not as outstanding as it was last season.
“That said, he is a top young talent with the mentality to make those improvements and United would be lucky to have him.”