The 22-year-old had an outstanding campaign as Stags made the play-off final at Wembley last weekend.
“I certainly need to look at the goalkeeping situation,” said Clough.
“We would love to keep Nathan Bishop so we have already instigated a discussion with Manchester United about that.
“Ideally I think they want him to go into the league above, but if it's a lower League One club we are hoping to only be five or six places below them.
“Nathan knows us and I think he enjoys working with Seamus McDonagh.
"That has got to be one of the major attractions for him.
“He is working with one of the best goalkeeping coaches and one of the most experienced goalkeeping coaches in the country.
“He has just played 52 games for us, which I think is more than he has played in his career.
"Do the same again next season and you will improve again.”
Stags’ veteran keeper Marek Stech is out of contract this summer and Bishop’s planned start of season back-up keeper George Shelvey ended up going back to parent club Nottingham Forest early as his season-long loan was terminated in January. So Clough may need to find two keepers this summer.