The retired striker believes the starlet has the potential to be as good as some of the Reds' greatest ever wingers and hopes Sterling could eventually be spoken of in the same breath.
Aldridge also challenged Stewart Downing to regain his place in the side after losing his spot to Sterling for the visit of the champions.
"Over the years our club has had some very special wingers," the 53-year-old said in his column for The Liverpool Echo.
|REDS SHOOT DOWN THE GUNNERS|
|14/1||Liverpool are 14/1 with Bet365 to beat Arsenal 3-1 on Sunday|
"From Billy Liddell to Peter Thompson, Steve Heighway, Ian Callaghan, John Barnes and Steve McManaman. It’s been a while since we’ve had anyone in that bracket but hopefully in time Sterling will prove he deserves to be mentioned alongside those names.
"He certainly has the potential. I want to see him play week in week out now and I believe the winger is going to get better and better.
"Stewart Downing will have got a fright after losing his place to a kid. He’s got to knuckle down and try to get back in."
Aldridge also lamented Liverpool's defensive lapses, which cost the Reds all three points at Anfield on Sunday.
However, he was encouraged by the performance in general following the previous weekend's 3-0 loss to West Brom - and said Brendan Rodgers and his charges can look forward to a successful season.
He added: "Liverpool deserved more on Sunday but if we keep playing like that – and tighten up at the back – then I’m optimistic about what we can achieve this season.
"We can certainly be happier than we felt after the opening weekend of the new season."