"We think the Trent Bridge area is the best place for the club to remain and we will work with them to achieve a settlement that allows that to happen," Mellen told the BBC.
"We're not ready to give up talking or end negotiations and whether that's with the chairman or the owner, we'll do what is necessary."
Forest chairman Tom Cartledge had previously said: "We find ourselves in a position where for the first time we're having to consider whether the future is going to be away from the City Ground
"In the future, football clubs' wage bills are going to be very heavily linked to revenue.
"If we can't grow the revenue, there is a realistic chance we cannot achieve our objectives and grow the playing side and give the manager the resources he needs.
"Unless we start to see some significant progress, it is now having to be a realistic discussion point as to look elsewhere.
"I'm frustrated, the owner is frustrated, because what he wants to do is give back what he promised the people of Forest, which is growth on and off the field and not to be able to do that is tough."