The £20million winger has struggled since arriving at Anfield from Aston Villa in the summer of 2011, so much so that Reds boss Brendan Rodgers suggested he was able to leave in January if a decent offer came up.
But Downing is hoping he can put some good performances forward in a bid to remain despite a mediocre beginning at the Merseyside club.
"I wanted to stay, I didn't want to leave, but it was out of my hands," Downing told Sky Sports.
"I was out of the team and frustrated and I said, if something big came up, I'd look at it. We had that conversation and, to be honest, I thought I was on my way in January.
"I was a little bit surprised when [Rodgers] said I could go. He came in and was pleased with me at the start and then, all of a sudden, things changed quickly and I could go.
"The good thing is we have had open dialogue. I speak to [Rodgers] if I have a problem and, if he has something to say to me, he can speak to me, so from that point of view it has been good.
"He has been straight with me and said if something comes up in January them we'd look at it but if he's saying I'm staying then it's a funny old game.
"The only thing I can do is play well and make him keep me and pick me and that is all I am trying to do."