Regarded as one of United's most experienced players, the 35-year-old's time at Bramall Lane is to come to an end following interest from other clubs.
Starts were hard to come by for Cresswell last season for the Blades, and he is now seeking pastures new.
After Saturday's 3:1 friendly victory over Bury at Gigg Lane, manager David Weir confirmed that he wouldn't be featuring in his plans for the new season.
"I don't think it's done (a deal) quite yet, but it looks as though Richard will be leaving.
"There's a few clubs that are interested in him so that'll be his choice at the end of the day.
"The fact that he has a lot of clubs interested tells you a lot about him."
York City, familiar surroundings for the Yorkshire-born striker, seems to be a possible destination.
Cresswell spent the back end of last season on loan at Bootham Crescent and helped steer the Minstermen away from League Two's trapdoor.
Cresswell has partaken in United's pre-season campaign this summer, as Weir explains:
"He came on the trip up to Scotland with us and he did really well up there both on and off the field in regards to the type of professionalism he showed.
"Richard's been a great servant and I can't praise him highly enough in the time I've been here in regards to how well he's worked and how much of a benefit he has been to the younger players.
"It looks like Richard will be leaving and he goes with our best wishes."