Agger's agent confirmed earlier this week that Liverpool have rejected a bid from the La Liga champions for the defender.
However, despite the interest from Spain, Rodgers believes the 28-year-old is committed to the club having been appointed as the side's vice-captain last week.
"Daniel has given me his word that he loves Liverpool and I will expect him to be here. He had chances to leave, but told me as long as we wanted him here, then he wanted to stay," Rodgers told The Mirror.
"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."
With the Luis Suarez transfer saga still rumbling on for Rodgers, he remains determined to ensure another key player does not edge closer to an Anfield exit.
"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," the Northern Irishman said.
"There have been a couple of inquiries, but we have made our position clear."
Agger has made 209 appearances for Liverpool in all competitions since joining from Brondby in 2006.
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