Like father, like son could ring extra true in the May family ... 'cause fresh off winning a national championship with Michigan, Charlie tells TMZ Sports he's exploring a career in coaching -- just like his pops/coach Dusty!!

We caught up with the senior guard as he worked a celebratory shift with fellow hooper Nimari Burnett at Raising Cane's in Ann Arbor on Thursday ... and asked him what's next after the Wolverines cut down the nets against UConn earlier this week.

Waiting for your permission to load the Instagram Media.

He explained his playing days are over ... and now he's going back to school in more than one way -- he'll be a graduate assistant at Georgia as he doubles up on his degrees.

Charlie -- who also played at UCF -- and Dusty joined Michigan in 2024 ... and just two years later, they brought the trophy home.

Basketball is in the blood -- Charlie's older bro, Jack, was also a college hooper ... and his lil bro, Eli, was the team manager.

The tourney was big for the whole family ... and Charlie said it added another layer of joy having them around for the "surreal" experience.

We also had to ask if Pops is tougher on him on the court or at home -- watch the clip to hear his answer!!