The England winger started just one Premier League game before November 25 and was told he could find another club in January.
But injuries and loss of form elsewhere in the Liverpool squad provided a reprieve, and Downing has featured regularly since the transfer window closed.
"That's football for you," he said. "Me and the manager have always had open conversations and I found it difficult at the start of the season because I didn't play, it wasn't that I wasn't playing well.
"Once I got in the team and had a run of games my form picked up and I think the team got better and better and we've had some good results, especially after Christmas.
"There have been some positive signs and personally I'd like to stay but that is the manager's decision.
"If we keep this team together - and I am sure the manager will strengthen -then we can have a right good go next year, that will be the big test.
"The change in manager, the change of players coming in and the change in the way we play we were not going to win everything this season. Next season is obviously the big test for us."