Rodgers has suggested Suarez owes a debt to the club and the city.
He said: "The support he has received from the supporters and the people of Liverpool has been unrivalled.
"In this period of time he's missed a lot of games for the club through various reasons. The people have stood by him like a son and really looked after him.
"Whatever happens in the coming weeks that will be in his mind because it's something you can never forget."