Valencia president Anil Murthy has told Real Madrid that Rodrigo will only leave the club this summer if his €120 million release clause is met.
A reported target of several European clubs, the Spain international had a strong 2017-18 campaign at Valencia, scoring 16 goals and assisting four more in 37 league appearances.
Marca claim that Valencia are prepared to sell Rodrigo for a fee starting at €60m, half of his buyout clause, but Murthy denied such claims.
"Everyone is aware that [Real Madrid coach Julen] Lopetegui knows Rodrigo but what happens at Madrid, we do not know," he told Tribuna Deportivo radio show. "What I do know is three things: Rodrigo is a very important player that has a very high value, he wants to play here with us and he has a €120m release clause."
Rodrigo has four years left to run on his Valencia contract, and declared after the World Cup his wishes to continue playing for the club.
When asked if Valencia, who are competing in the Champions League this season, would be willing to negotiate Rodrigo's departure, Murthy was firm on his stance.
"We didn't place the €120m clause without analysing the market," he said. "Things change every day and we have to wait and see."
Valencia coach Marcelino is optimistic Rodrigo will remain with the club.
"Could he go to Real at the request of Lopetegui? That's something you'd have to ask Lopetegui about," he said. "I think he will stay here. He looks convinced, excited and motivated. If Real Madrid want him, then there is a release clause."
Lopetegui worked with Rodrigo as manager of the Spain under-21 side as well as the senior team before his sacking on the eve of the World Cup.
Valencia have strengthened their attack with the signing of Kevin Gameiro from Atletico Madrid, and Michy Batshuayi, who has joined on a season-long loan from Chelsea.
"With 15 days to go before the transfer window ends, we have our squad," Murthy said. "We have a very competitive team. We haven't bought expensive players, we haven't done crazy things.
"We had a plan and we have signed the players that were on the list that we wanted. I'm certain we have a team that can compete at the highest level."