The wide receiver is due to be a free agent after playing the final season on his current deal with the NFC West team.
The Rams head coach told the St Louis Post-Dispatch: "We've got a number of unrestricted free agents on our roster that we want back, and Danny would be one of them. [Steven Jackson] would be another.
"We've got plenty of time. The process is ongoing. We're communicating with their agents and so on and so forth.
"There's options out there. The free-agent market, there's options out there, and it's a great draft for a receiver this year."
Amendola played 11 games in the 2012 season, scoring three touchdowns for 666 yards.