Cresswell is one of the players who could be a target for other clubs this summer, along with the likes of David McGoldrick, but McCarthy is staying relaxed about the situation.
He regards Cresswell as the finest left-back in the Championship and has no intention of letting him go, but he also has a lot of faith in understudy Mings.
The 21-year-old Mings was recruited from non-league side Chippenham Town just 15 months ago but has impressed when called upon and McCarthy believes he is ready for a more regular role.
"I've said on numerous occasions how much I like Ty," said McCarthy in the Ipswich Star.
"He's taken the step up to this level in his stride and I've had to speak to him a couple of times because I think, in lots of other teams, he'd be playing. Here though he's behind the best left-back in the league."
Asked if he expected there to be bids for his best players this summer, McCarthy said: "Maybe, I don't know. I suppose we're at that time - Cressy, David McGoldrick; there'll be a few. If the phone rings I might just ignore it!"
Southampton, West Bromwich Albion, Hull City and Fulham have all reportedly sent scouts to watch Cresswell, who has provided 13 assists in the Championship this season.