The midfielder joined the Reds for £20 million in the summer of 2011 but has struggled at Anfield before stepping things up with his first Premier League goal for the club against Fulham.
"I wanted to stay, I didn't want to leave, but it was out of my hands," Downing explained to Sky Sports regarding being told that he would be allowed to leave in the winter transfer window.
"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.
|35/1||Stewart Downing is 35/1 with Bet365 to score anytime in a 2-1 Liverpool win over Stoke City
"I don't know who makes that decision but one minute I was being told I was doing well and the next I was told I could go."
The winger noted that facing the prospect of being sold may have helped him to turn the corner.
"It was a bit confusing but it is a kick up the backside," he observed. "I then had nothing to lose as I was going. If it was a gee-up for me then maybe it's worked because the performances are coming now.
"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."