The 23-year-old has been on loan with the Valiants since November, and Martin Foyle is keen to make the move permanent.
"I can confirm we have accepted a bid from Port Vale for Clayton Fortune, although that was part of the loan agreement that took him there," City chairman Steve Lansdown said.
"It is an undisclosed five-figure sum, while we also have a sell-on clause in the deal. It is now up to Clayton to agree terms with Port Vale."