The Blaugrana are in the market for a centre-back and reports suggest that the Danish international is among those on their wanted list.
However, Rodgers has revealed that when he arrived at Anfield last summer, the 28-year-old promised his future to the Reds.
"This is all about loyalty," Rodgers told reporters. "When I first came to Liverpool, Daniel was one of the players who I talked to first.
"That day, he promised me that he would stay as long as I wanted him to stay - and he has never changed his stance on that promise."
Agger joined Liverpool from Brondby in 2006.