After six months on-loan with AS Monaco last season, Silva is eager to find more regular first team football.
Rodgers revealed: "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."