Sterling was a fleet-footed menace throughout the 5-1 victory at Anfield, scoring Liverpool F.C.'s third and fifth goals and tearing into the visiting defence with his searing pace throughout the match.
"Raheem Sterling was incredible. He's just turned 19 years of age. I don't think there's a better winger in England at this moment in time. He's absolutely phenomenal," Rodgers said on the club website (www.liverpoolfc.com).
Sterling, who arrived at Liverpool F.C. as a 15-year-old from Queens Park Rangers, made a big impact when he first won a regular place in the side under Rodgers early last season and made his England debut in a friendly against Sweden in 2012.
But tiredness and a loss of confidence combined to lessen his effectiveness as the campaign wore on and Rodgers decided to withdraw him from the firing line and rest him for the tail-end of the season.
He has rediscovered his form in recent weeks, cementing his spot in the side with a string of confident displays and Saturday's goals were his fifth and sixth of the season.
Team mate Jordan Henderson says his work at both ends of the pitch is likely to have caught the eye of England manager Roy Hodgson.
"He's a great player," Henderson said. "Defensively he works really hard for the team and going the other way he's fantastic. Scoring goals is important for any forward player and he's adding that to his game, which is brilliant.
"I think he's got every chance of going to the World Cup in the summer. He's still a young lad, but at the same time, he's mature enough and if you look at his performances, he's one of the stand-out players of the season for me.
"The way he's played in the last few weeks has been unbelievable. I'm sure the manager (Hodgson) will be keeping a close eye on him."
Liverpool F.C.'s superb performance against Arsenal was characterised by their relentless pressing of their opponents, looking to win the ball back high up the pitch before launching swift counter-attacks.
"A big part of our game is the intensity and it's about getting the ball back quickly when we lose it," Henderson added.
"I felt as though we did that well, especially in the first half. We won it back and a couple of our goals came from that. So that's pleasing."
Liverpool F.C., who are fourth in the Premier League and trail leaders Chelsea by six points, face struggling Fulham on Wednesday.