Goalkeeper Liam Gooch, defender Stephen O'Donnell, midfielder Danny Green and forwards Zane Banton and Craig Mackail-Smith will leave the club on 30 June.
But keeper King, 19, and defender Potts, 23, are set to stay, while the club's option on Frank Musonda's contract will be taken up.
Luton were beaten by Blackpool in the League Two play-off semi-finals.
Youth team captain Kavan Cotter, who made his senior debut in the EFL Trophy last August, has been offered his first professional contract with the Hatters.
Luton Town have released five players, but Craig King and Dan Potts are to be offered new contracts.