Agger still has three years left on his contract with Liverpool.
Reports have suggested that Barcelona have made a bid for the Danish defender.
"Daniel has given me his word that he loves Liverpool and I will expect him to be here," Rodgers told the Daily Mirror. "He had chances to leave, but told me as long as we wanted him here, then he wanted to stay.
"He's been brilliant, that is why we have given him the vice-captaincy. The one thing I got from him from the very first conversation is loyalty.
"That is why he signed a new contract and committed himself to the club, and why we gave him a new contract - because we want him to be part of our future.
"He is important to the way we play, and he has been central to the way we work since I came here, and he knows that. There have been a couple of enquiries, but we have made our position clear."