The winger's struggles since joining for £20 million in the summer of 2011 had prompted the Reds boss to suggest that he could be sold in January but the England man has improved his performances of late and is keen to remain at Anfield.
"Over the last six or seven weeks, his consistency has been outstanding and he has been asked to play in a number of different positions," Rodgers said of Downing to the media.
|35/1||Stewart Downing is 35/1 with Bet365 to score anytime in a 2-0 Liverpool win over Stoke City
"He's at an age where he can be at the top of his game.
"He is an outstanding player and, mentally, he is really in tune with the team and the work. When he is playing like he was [against Fulham], there are not too many players who can play on the sides better than him. Hopefully he can continue with his form.
"He's still got a few years left on his contract here. We don't want him to go anywhere - all we have ever asked is that every player can be at the top of their game and be as good as they can possibly be.
"If he continues along the lines that he currently is, he'll be here for a number of years yet.
"Confidence is the key to everything and there's no doubt that his confidence levels are very high at the moment but he knows that to maintain that he has to continue to work hard and keep doing things consistently well."