After a flying start to the season, Rennes are eager to capitalise by adding to their midfield.
France Football says they're planning a move for Silva, who spent the second-half of last season on-loan with AS Monaco.
Just yesterday, Foxes boss Brendan Rodgers stated: "I had a long talk with Adrien and I know where he stands and what he thinks.
"He is a seasoned 30-year-old and players like him want to play. The market window is open for a few more weeks and there may be something for some players in this position.
"If so, they and their club representatives will be able to analyse."