The 24-year-old has been linked with a step up into the Premier League for some time and 2014 could be the year in which he makes that leap.
West Bromwich Albion are the latest side reported to be weighing up a summer approach for a player who only committed to fresh terms at his current employers in December.
Ipswich are, however, aware that their hand could be forced and that deal broken if a sizeable offer is tabled.
Those contemplating an approach have already made initial contact with the Portman Road outfit and Mick McCarthy concedes that Cresswell could be on his way once serious negotiations are opened.
He said: "There is interest, I can't deny that, as he is a good player, but if there are any bids, I won't be telling you.
"He was getting the plaudits last season for being the best left-back in the Championship and at some stage, if someone comes in and the deal is right, then it becomes an irresistible force.
"He is under contract, but that becomes a negative as the player sees there has been a bid for him that everyone else seems to think is fair.
"He may feel he's done his time and want to move to better himself. If that's the case, it's hard to stop.
"If he does go I will shake his hand, thank him for his efforts and crack on and bring someone else in, that's how it works. It would have to be the right bid though."