Tierney only penned a new six-year contract with the Hoops last season, but the 21-year-old's form has led to suggestions that the likes of Manchester United and Tottenham Hotspur are interested in his services.
In May, the Scotland international insisted that he was "not in any rush" to leave Celtic, and Hartson sees no reason why the left-back should move on in this summer's transfer window.
"Time is on Tierney's side. His price tag is only going to go up. He could play with Celtic for another year, gain some more experience, and then make the move we all knew would come," Hartson told the Evening Times.
"He might go. If he does, good luck to him. He will get a big club, a big pay rise and he's already part of Celtic folklore.
"However, it is worth repeating that there is nowhere better to play than Celtic Park. Ask anyone lucky enough to pull on that jersey. The Premier League is one hell of a temptation. But Celtic is a hard place to leave."
Tierney scored four times and registered 11 assists in 55 appearances for Celtic last season.