The Reds vice-captain has fallen down the pecking order in recent weeks after his rib injury allowed rival centre-halves Mamadou Sakho and Martin Skrtel to forge a partnership.
Brendan Rodgers signed the France defender in a £16m deal from Paris Saint-Germain in the summer as well as Portuguese youngster Tiago Ilori and Kolo Touré.
But Agger, 28, is determined to force his way back into the starting line-up and help the Merseyside outfit win some silverware this season.
“In January I’ll have been at Liverpool for eight years,” Agger is quoted as saying by Liverpool Echo.
“If you count how many central defenders have gone through the system during that period you’ll need to use more than one hand. I’m standing there still.
“For me (staying at Anfield), it’s also about making the team as strong as possible because I’m hungry to win something.
“I believe winning things is possible. I’m interested in being part of a squad of 25 strong players, and those who the club bought in during the summer clearly help raise our level.
“We have a great team, and if I can win something it will be great. Liverpool is a huge club.”
Agger, who arrived at Anfield from Brondby for £5.8m in January 2006, signed a two-year contract extension back in October 2012 to keep him at the club until the end of the 2015-16 season.