The Hoops have been keeping tabs on the Northern Ireland midfield ace for months and could make their move once a new manager is finally installed at Parkhead.
But Saints chairman Steve Brown is adamant the 21-year-old will not be going on the cheap.
Boss Davidson still holds the record for the highest transfer fee banked by the McDiarmid outfit following his £1.75milllion move to Blackburn back in 1998.
But Brown says it will take more to persuade him to release McCann.
"There's been a huge amount of interest in Ali," he told Radio Clyde. "He's been consistent over the last two seasons and is going away with Northern Ireland on international duty.
"He's played against Italy in the last international break and he's a class act.
"Our transfer record is £1.75million and Ali will not be leaving for any less than that.
"We don't want players to leave when we have a successful team. Selling players is one thing but replacing them is another - it's a huge challenge to get the same calibre of player back in."
It has been a dream season for Saints on the back of Davidson's Hampden heroics.
Tommy Wright's former number two overcame a tricky start to make history by leading St Johnstone to both the Betfred Cup and Scottish Cup in his rookie year as boss.
And Brown expects it will not be long before he starts receiving calls from potential suitors interested in securing Davidson's services too.
"I don't think there's a limit to what Callum can achieve," he said. "He's demonstrated what he can do with a club the size of St Johnstone with limited resources what can be achieved.
"He's very good at his job, he's meticulous, he knows the game inside out.
"I think he will kick on now. I'd prefer if he stayed here but the reality is that if he keeps doing well, he will move on.
"It was a difficult first few months for Callum but I wasn't concerned because I like to think I know a little bit about football.
"The way we were playing, we were creating loads and loads of chances.
"But yeah I did have to speak to Callum. As usual with football fans, there is a lot of negativity going about - 'It's the wrong guy we've appointed' and everything else.
"I just told him to blank out the noise, concentrate on what he was doing, don't pay any attention to the negativity.
"If anyone is going to decide whether he goes or stays, it was myself and I told him he had my backing 100 per cent."