The centre-back has been a target for Barcelona, with the Reds reportedly rejecting a £15m bid for the Dane earlier this week.
However, Rodgers said that loyalty is a key characteristic of Agger and claimed that he expects the former Brondby man to remain at Anfield.
"The one thing I got from Daniel Agger from our very first conversation is loyalty," Rodgers told the Liverpool Echo.
"He has given me his word that he loves Liverpool and I will expect him to be here this season. Daniel has been brilliant for me, he is one of the players who is being considered for the vice-captaincy."
Liverpool end their pre-season preparations with a friendly against Celtic tomorrow.