In the first half of the season the England international could hardly get a game and when he did it was sometimes at left-back.
Rodgers told him in November he could find another club when the January transfer window opened, but injuries provided an opening in the team and the 28-year-old seized his chance.
"That's football for you," said Downing.
"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."
Downing believes that upturn in performances since the new year points to a sense of optimism for Rodgers' second campaign in charge.
"I think overall it has been a decent enough season," he told BBC Radio Merseyside.
"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 (league 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."
Fellow midfielder Jordan Henderson believes his hard work on the training ground has been rewarded with the best goalscoring campaign of his career.
But the 22-year-old is not satisfied with his tally of six, scoring three in his last half-dozen games, and intends to become more of an attacking force next season.
Henderson is the club's fourth-highest scorer this season, with the leading two, Luis Suarez (suspended) and Steven Gerrard (injured), unavailable for the final two matches.
The latter's absence because of a shoulder problem means Henderson is likely to get the chance to play in his preferred central role at Fulham on Sunday.
But there is no doubt his all-round game has improved and he wants that to continue.
"It's always important for midfielders to get goals. Hopefully I can keep working on that and get a few more next season," he told liverpoolfc.com.
"Scoring goals has been brilliant for me on a personal level, but I think the team has definitely progressed throughout the season and we can only get stronger and better and we look forward to next season.
"We've played some really good football and won some really good games.
"We're definitely progressing all the time and we'll look to continue to do so in the last two games and next season."