The Denmark centre-back was hampered by injuries last Premier League season and had limited game time under manager Brendan Rodgers.
With Southampton's Croatian international Dejan Lovren also set for a move to Anfield, Agger will face even more competition for his place.
Agger, 29, said it was an unacceptable 2013-14 campaign from a personal perspective and he was considering his options.
"It is no secret that I had problems last season and I am considering things," he 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."
Agger refused to rule out a return to Brondby, while Napoli are also believed to be interested in his services.
On Thursday, Rodgers described Agger as "one of the best players" at Liverpool and has a role for him at the club.
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