Speculation surrounding the highly-rated Scotland international has raged for some time.
Despite having over 160 club appearances to his name, and 12 caps for his country, Tierney is still just 21 years of age.
He is considered to be destined for the top, with it only a matter of time before the interest being shown in him from afar leads to a big-money bid being tabled.
Celtic legend Petrov told the Daily Record of a player who is under contract until 2023 but continues to be linked with the likes of United: “You don’t go under the radar if you are consistently one of the top performers.
“I don’t know if it will be this summer or next but I do think at some point Celtic’s resolve will be tested.
“And if a huge offer comes in the reality is you have to take it. It will take big money to get him. I don’t know how much but it will be no problem for a Man Utd or whatever.
“The boy just has to keep doing what he is doing. Getting into the Champions League can be so important for his development.
“He has the potential to go on and be world class. He could go to a Man Utd or any other top-level club because he’s been brought up having to play under pressure.
“Like all good players he has not just survived in that environment but has flourished and those who have the temperament to deal with that are the guys who make it to the top.
“He has shown he can cope at European level. In the Champions League he has been excellent. But it is also about the way he behaves on the pitch. He has shown he is a leader.
“He has captained his country and he has captained Celtic. That is special for being only 21.
“He will get better all the time. As an ex-Celtic player and a Celtic fan I want him to be here for as long as possible. But that is not how football works.”
Tierney has made no secret of the fact that he wants to spend as long as possible at Parkhead before making a move elsewhere.
As a Celtic academy graduate, he has strong ties to the Glasgow-based outfit and is in no rush to take on a new challenge.
That issue may be forced, though, if his list of suitors continues to grow and his consistency in Scotland eventually sparks a scramble for his signature in an upcoming transfer window.