Villa have made their move for Heaton after Championship Stoke refused to drop their £25million price tag on England shot-stopper Jack Butland, says the Mirror.
But Villa have told Burnley they will not pay over the odds for Heaton, who is 33 and only has one year left on his contract.
And a move to Villa could be sealed later this week to make Heaton Villa's seventh summer signing.
Villa could also seal an £8 million deal to bring Trezeguet from Turkish side Kasimpasa. Trezeguet operates as a winger at the Turkish club, netting nine goals in 29 league games last term.