Downing appeared on his way after an early season rocket from Rodgers, but has won over his manager in the second-half of the campaign.
He told the official Liverpool FC magazine: "All I need to do is look at the bench to remind myself that I have to keep performing well.
"There is real competition for places, especially since Daniel (Sturridge) and (Philippe) Coutinho arrived in January. You have lads like Raheem (Sterling) waiting for a chance too. It means if you're not playing well you'll be hauled off.
"I'm sure the manager will also be looking to add to the squad in the summer.
"He's told me I'm part of his long-term plans, which was great to hear. Now I have to ensure that continues to be the case."