Capp has yet to make a first team appearance at United, and is third in line behind Paul Musselwhite and Tommy Evans.
He follows in the footsteps of Steve Torpey and Cleveland Taylor in committing himself to the club.
Ian Baraclough has had his contract extended, while Paul Musselwhite, Andy Parton, Paul Hayes, Peter Beagrie and Michael Rankine are mulling over contract offers to stay at Glanford Park.
Talks with Nathan Stanton and Richard Kell are 'ongoing'.