Shearer scored 260 goals during his time in the top flight of English football and he believes that Manchester United forward Rooney can eclipse that total.
The former England captain told BBC Radio Five Live: "I really think Wayne could challenge that 260-goal mark.
"If he continues in the rich goalscoring form he's in right now, I think he'll get close.
"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."
Rooney has scored 143 Premier League goals since making his debut for Everton in 2002.