The Rams have agreed a deal with former trainee Grant to return to the club this summer when his contract at Championship rivals Burnley expires.
Clough described the opportunity to sign Grant, 30, as "too good to turn down" and both Fielding and Legzdins, who are both about to enter the final year of their contracts, could leave Pride Park during the close season.
"Lee is going to be our number one," said Clough. "The problem is they both want to be number one as well.
"I think they have an opportunity now to see what is out there for them. It is harsh on the other two, who have both been fighting to be number one, but the opportunity to sign Lee was too good to turn down.
"If offers come in, Frank and Adam will both be allowed to leave. We would love to keep one of them as the number two but, unfortunately, they don't want to do that.
"Both have had a taste of first-team football and once you have had that taste, you don't want to sit on the bench."
Injury and suspension problems have meant that Fielding and Legzdins have both had runs in the team this season.
Fielding, first choice for the majority of last season, also began this campaign as number one before suffering a groin injury at Middlesbrough in October which opened the door for Legzdins to make 30 consecutive starts.
Legzdins was then replaced at the start of March, but a red card for Fielding in the home victory over Peterborough on April 20 gave him another chance.