Shearer hit 260 goals in the top flight during his career and that was some 73 more than the man who was in second place, Andy Cole.
Rooney currently has 143, but Shearer is of the opinion that there is a lot more mileage left in Rooney.
"I really think Wayne could challenge that 260-goal mark," he told BBC 5 Live. "If he continues in the rich goalscoring form he's in right now, I think he'll get close."
"Wayne hasn't always looked like a natural goalscorer, but then I struggled for regular goals in the first few years of my career too, and he's still only 26.
"If he can steer clear of serious injuries - I had three which cost me more than two years of my career - for the next few years, he's definitely got a chance."