The two have not seen eye-to-eye since Hodgson took over at Anfield, with Agger criticising the Reds' direct style of play earlier this season. That row was defused when Agger was ruled out for three months with a damaged calf but, after returning to the team for the 2-1 win over Bolton, he has again taken issue with his boss.
"I still have three years on my contract but it's not me who decides if I'm playing," he said. "But if I'm not playing and I'm not injured, I have no reason to be here. I'm 26 and I feel I can play regularly at this level at this club. So if I'm not going to play and be on the bench for a while, obviously I'm not interested in being here. Then I must see what options I have."
Elsewhere, Hodgson has called for his players to show more belief as they bid to turn their season around. The Reds are currently in tenth place, just five points clear of the relegation zone.
"We've got to build up our sense of belief in ourselves and what we're doing," he said. "We need to have more faith in our play - but I thought that was very evident against Bolton. Taking the game to them and not getting hit in the counter shows a lot of character, faith and belief.
"Football is technical and tactical quality but there's a third dimension - spirit, guts and determination."