Agger has come out with some comments that are likely to fuel speculation recently.
The Reds’ defender was signed from Brondby in 2006 by Rafa Benitez and there are reports that they could be reunited at Napoli, but there have been no offers for the Danish defender so far.
Earlier this week, Agger made some comments in the Danish media saying that he will be nobody’s third choice at the club, and missing out on key encounters against Manchester City and Chelsea may have been a sign that Brendan Rodgers didn’t think he was good enough.
The defender said: "I can't go and put myself on the team sheet.
"It definitely wasn't great to be left out, but I don't make the decisions.
"I think it is because the manager doesn't think that I'm good enough."
Agger reportedly attracted interest from Barcelona and Manchester City last summer but with the arrival of Mamadou Sakho at the club, combined with his own injury problems, Agger hasn’t been getting the first team opportunities that he perhaps would have liked, having made 20 appearances in the Premier League this term.
The Liverpool defence is likely to have several changes this summer following on from a campaign where the side conceded 50 goals in the Premier League alone, and with the club returning to the Champions League for the first time since 2009, any money raised from the potential sale of Agger is likely to be used to buy new players.
During his time at Anfield, he helped the side reach the Champions League final in 2007, as he scored a crucial goal in the semi-final against Chelsea as well participating in the FA Cup winning side in 2006 and the League Cup side in 2012.
But injuries have blighted his time on Merseyside, and after another season where he picked up more injuries, and Mamadou Sakho having had a season to settle in, the club might feel it is right time to cash in on Agger going forward.