Sturridge has showed his sharpness by slotting home two of his five goals for the club so far from close range.
He tucked a loose ball beyond David De Gea against Manchester United at Old Trafford in January before turning home Stewart Downing's cross in front of the Kop against Norwich.
His ability to ghost unmarked into the box was just one of the many traits Rush picked-out as he delivered a shining appraisal of Sturridge's first two months at Anfield.
"He has been absolutely fantastic - just what the supporters have been looking for," Rush told Liverpoolfc.com as he took time out from a Garuda Indonesia coaching clinic in Jakarta.
"He's a natural goalscorer. The goal he scored against Manchester City, there was no backlift, it was a fantastic strike.
"Before he came, the opposition focused mainly on Luis Suarez and Stevie [Gerrard] but with Sturridge, there's an added danger. He seems to gel well with Suarez and Stevie.
"He gets the tap ins as well. [In the past] we've had plenty of great shots where the ball has hit the post and come back or the keeper has saved and we've just been looking for someone to come along and tap the ball in. Sturridge does that.
"Also, his first touch is incredible in and around the box. He's very skilful and he's got a bit of pace. He can drift out to wide left, out to wide right and he can play through the middle."
In the seven games Sturridge has started alongside Suarez, their bourgeoning partnership has conjured 10 goals for Brendan Rodgers' side.
Link-up play between the duo was at its most potent when Sturridge dummied a Lucas Leiva pass into the path of the Uruguayan, who swept home Liverpool's second against Norwich at Anfield.
And Rush explained how the pair both possess a footballing intelligence that will help their partnership blossom.
"The key to a successful partnership is both players having a footballing brain because it's all about how you read each other's game," he said.
"You can practise as much as you want on the training pitch but it's about how you link during the game.
"Sturridge will read Suarez and look for a rebound from his shots. If Suarez goes out to the right, then Sturridge can come into the middle or vice versa.
"I'm looking forward to watching their partnership blossom and I hope it will develop into one of those special partnerships but only time will tell.
"It certainly won't happen overnight - they'll have to work with each other in training, day in and day out."