Hereford pair Sean Canham and Janos Kovacs have rejected moves away from the club despite falling out of the manager's favour.
Both players were signed by former manager Simon Davey who was sacked after just 10 games. Current manager Jamie Pitman has said they are not in his first-team plans.
Chariman David Keyte revealed Canham, 26, and Kovacs, 25, refused to move to high-profile Conference teams.
Keyte said:"There is always speculation surrounding players but the only enquiries we've had have been about Kovacs and Canham.
"I've heard rumours about other players supposedly leaving, but those have been speculation and you hear rumours all the time in football. Kovacs and Canham have turned down about three moves each.
"We've circulated them widely and they've had interest from Conference clubs. One or two of the clubs interested in them would actually be bigger clubs than us. They have contracts at Hereford United and they have decided to stay put."