The 28-year-old has not made a single Premier League appearance for the Red Devils this season and could be allowed to leave the club on loan during the January window.
A recent report claimed that Lingard's representatives have held discussions with Nice over the possibility of joining the French club for the second half of the 2020-21 campaign.
However, Rivere has seemingly ruled the Ligue 1 outfit out of the race for the England international.
"We have seen a lot of names appear in the press without any merit. Our goal is to get our entire squad back together and we all aim to have a good second part of the season," Rivere told Nice-Matin when asked about the Lingard rumours.
"No, that won't be the case (expecting a big transfer in the winter market). The context is totally inappropriate. We know that the winter transfer window is very special and difficult. We had the opportunity to bring in William Saliba and we are delighted."