The Denmark international was hampered by injury problems last season and started just 16 Premier League matches as the Reds finished second in the table behind Manchester City.
Brendan Rodgers insisted recently that Agger remains a key part of his plans for the new season, particularly as the Reds face an increased fixture workload on their return to the UEFA Champions League.
And while the centre-back is determined to prove his worth to Liverpool, he is clearly unhappy at how the most recent campaign transpired.
"It is no secret that I had problems last season and I am considering things," Agger told Danish newspaper BT.
"How things turned out last season is not acceptable for me.
"I am here now and it is up to me to show the coach that I should play."
A return to former club Brondby has been suggested and Agger would not rule out a move back to the side he left in January 2006 to make the switch to the Premier League.
"Many things can happen in football and I do not want to exclude anything," he added.