The 29-year-old only made 20 Premier League appearances for Brendan Rodgers' side last season and does not want to spend any more time on the bench this term
The Denmark international made 20 Premier League appearances last season but faces further competition in central defence due to the imminent arrival of Dejan Lovren from Southampton.
Goal understands that Liverpool have been open to offers for the 29-year-old since May and Agger admits he could move clubs this summer.
"It is no secret that I had problems last season and I am considering things," the centre-half told BT.
"How things turned out last season is not sustainable for me. I am here now and it is up to me to show the coach that I should play."
Agger also claimed that he would not rule out a return to Brondby, where he came through the youth team ranks before joining Liverpool in 2006.
“If the time is right and there are some things that go up to a higher level I will not reject it,” said the defender.
“There may be many things in football but I would not rule anything out.”