The Manchester United outcast is expected to leave the club in the January transfer window and Nice had been touted as a possible destination for the Netherlands international.
However, the president of the Ligue 1 leaders denied rumours linking the Dutchman with the club, saying that he was out of their "financial reach".
"We looked at him, like a lot of clubs have, but it is extremely complicated… It is a situation which is out of our financial reach," Rivere told French radio station 'RMC'.
"You have a club that bought him for a certain amount that wants to sell him. When we looked at Depay, it was in another way, which is not possible today.
"He was bought very expensively by Manchester United, they want to possibly sell him and we cannot compete in this sort of situation".