After a lacklustre start to the season their form has been much-improved in the last few months, as Downing has enjoyed a more regular role in the starting line-up.
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"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,” he told BBC Radio Merseyside.
"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."
Liverpool are set to miss out on European football next season, but a run of one defeat in their last Premier League games has given Downing plenty of optimism for the next campaign.
"I think overall it has been a decent enough season," he added. "There has been a lot of change; the football is certainly better the way we play.
"If we keep this team together - and I am sure the manager with strengthen - then we can have 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.
"Last season we got the [Capital One Cup] trophy but we didn't finish high in the league because we didn't play well enough. But next season is obviously the big test for us."