The England winger has been one of Liverpool's best performers in the past weeks and has started each of the Reds' last 10 games.
But his upturn in fortunes only came after boss Brendan Rodgers told him he could leave the club.
Downing, 28, said: "I wasn't in the team or playing and he said to me maybe I could look elsewhere because I need to play at my age.
"I didn't totally agree, but I understood where he was coming from. Obviously he needs players who are going to play and not be sat about, but I thought in the back of my mind if I get a chance I can prove myself to him.
"Luckily enough, I did in the next week or so after that. Our conversations have been very open - if I'm doing well he will say so and if not, I'll be pulled aside and told what I need to do.
"It's the same for all the players. It's good for me and that's how I like it - to be told if it's right or wrong."