The winger has not featured for his country since May 2012, having struggled to break into Rodgers's starting lineup during the early part of his tenure in charge at Anfield.
However, the 28-year-old has featured on a more regular basis since Christmas and Rodgers believes that he has been playing well enough to catch the attention of England boss Roy Hodgson.
"I've been delighted with Stewart, he has come into the team and made the position his own. He has been absolutely outstanding," Rodgers told the club's official website. "There's no doubt about Stewart's qualities and what he's showing at the moment is that fighting spirit, doing all those things that we ask of every player in the team.
"It was a terrific goal at the weekend, how he read the game to press the centre-half and challenge the goalkeeper. It was a wonderful finish with his right foot. It showed his confidence level and how he's playing at the moment and we'll look to keep that going.
"If he continues this form, I'm very hopeful he'll play himself back into the England team."
Downing has made 34 appearances at senior international level.