The Ligue 1 side are in the 2020-21 Champions League and are reinforcing their squad with that in mind.
And they are searching for a defender with number one target Mohammed Salisu joining Southampton.
Godin, 34, has a wealth of Champions League experiences from his time at Atletico Madrid, with whom he won two runner-up medals.
At the moment, Rennes have only contacted Inter to learn the chances of signing Godin.
The Uruguayan arrived at the San Siro on a free transfer last year following nine memorable seasons with Atletico.
Godin made 36 appearances for the Nerazzurri last season, but there have been reports that he could be sold.