The winger's struggles since joining for 20 million pounds 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 told reporters. "I was delighted for him, because it was a top performance against Fulham [on Saturday]. He scored a goal, he created a goal and he was a threat. He played really well against Aston Villa at fullback.
"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."
Downing's play has impressed Rodgers to the point that he has expressed his desire to keep him at Anfield for the long haul, even after his current deal runs out.
"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," Rodgers said. "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."