The pair, who advise Sir Alan Sugar on the hit BBC show, have reportedly been offered £25,000 each to appear in the dance contest's next series.
A source told the Mail on Sunday, "Nick and Margaret are the unacknowledged stars of The Apprentice and more and more people have been watching it because of them.
"They have really interesting, understated personalities and some of their reactions to what the candidates do in Sir Alan's tasks are wickedly funny."
A BBC spokesperson simply said, "Nothing is confirmed yet."
Hewer, 64, is said to be on the verge of signing for the show and is hoping to persuade Mountford, a 55-year-old lawyer, to appear with him.