The free-scoring Posh marksman is expected to leave London Road this summer as he has just one year left on his contract.
The Scotland international enjoyed a blistering campaign with 27 League One goals as Peterborough made a swift Championship return.
Although Posh chairman Darragh MacAnthony recently stated no bids have been submitted, director of football Barry Fry says the 27-year-old has now been given permission to discuss potential moves.
"Craig's wanted by a lot of clubs and we have given him permission to talk with three of them this week," confirmed Fry.
"He is scheduled to meet them with his agent and then it will be down to him. But he is in no rush and I wouldn't be surprised to see other clubs show an interest soon.
"I wouldn't mind seeing Craig in our side at the start of the season. We could still sell him before the end of the August deadline. But it really is down to Craig and what he does.
"He may get a fabulous offer from the first club he sees and decide to move there, but I'd be surprised if anything happens before the weekend."
Wigan were also reported to be in the hunt for Mackail-Smith but it is understood their interest may have now cooled.