Reports have suggested Grainger - released by Tynecastle boss Gary Locke last week as he strives to slash his wage bill - had attracted the interest of Saints manager Danny Lennon.
But the Scottish League Cup winners have distanced themselves from a move, with chief executive Brian Caldwell insisting the player was "not on our radar".
The 26-year-old has been invited to pre-season training with League One side Sheffield United and the Buddies expect the former Gretna, Dundee United and St Johnstone full-back to remain in England next season.
Caldwell said: "I spoke to our manager Danny Lennon when I heard Grainger had been released by Hearts. However, we understand he's going south and will be training with Sheffield United. Even if that doesn't work out, I think he wants to give England a go so he's not a player that is on our radar right now."
However, Caldwell says the club are keen to bring in two goalkeepers, a left-back, a left-sided midfielder and another striker this summer.
Saints have waved goodbye to Newcastle duo Paul Dummett and Conor Newton after the completion of the duo's loan spells, while Portuguese striker Esmael Goncalves has returned to Rio Ave following his temporary switch.
Goalkeeper Craig Samson, meanwhile, has rejected a new deal to sign for former club Kilmarnock, and Lennon has also released Graham Carey, Sam Parkin, Sander Puri, Dougie Imrie and Grant Adam.
Caldwell confirmed Lennon is hopeful of adding to his squad further after signing Dundee playmaker Gary Harkins, but denied he would be making moves imminently.
"We have got a few irons in the fire and are working on a number of things at the moment," the St Mirren chief executive said. "However, there is nothing concrete to report on and I don't see that changing any time soon."
- Sports & Recreation
- Brian Caldwell
- Danny Lennon
- Sheffield United