The England international has struggled to find a place in the first team all season and has found himself filling in at left-back on occasions.
Downing has been involved more in recent weeks, starting five of the last six matches in all competitions, but is not happy to play a bit-part role in the future.
"The manager has said I can leave if I want to," the 28-year-old said in a frank interview with Liverpool's matchday programme ahead of Saturday's visit of former club Aston Villa.
"But then all of a sudden, I've come back into the team. It's a strange situation.
"I've played for a long time and there are spells when you can be in and out of the side.
"At the minute, I'm trying to play as many games as possible.
"If that doesn't happen, I'm at an age where I can't be sat around. I need to play and the manager understands that.
"That's how the situation is and we'll have to see what happens in January or the summer."