Newcastle legend says that Lukaku will leave this summer, but he will not be cheap.
Everton's Romelu Lukaku
Lukaku's future at Goodison Park has been cast into doubt after refusing to sign a new £140,000-a-week contract with the club, as reported by the Telegraph.
Several Premier League sides are said to be keeping an eye on the Belgian, who tops the scoring charts with 21 goals, with Chelsea and Manchester United leading the way - according to the Independent.
Shearer says that Lukaku will be on the move at the end of the season, but if any of the "big boys" want to sign him it will cost significantly more than the £28m the Toffees paid for the 23-year-old in 2014.
Alan Shearer poses during the unveiling
"The impressive thing is that this is his fifth full season and he is on target to play over 30 games in every season, which is superb," the former Newcastle United forward said on Match Of The Day.
"I do think he'll go. I think the big boys will come sniffing for him. I think Manchester United will be looking for a forward or two, as will Arsenal and Chelsea.
"He's 23 years old, got a fantastic goalscoring record. They paid £28m for him? When you look at the prices now, you're talking £60m, £70m?"
Everton's Romelu Lukaku celebrates scoring their first goal with Everton manager Ronald Koeman
Everton manager Ronald Koeman told the BBC that the club "will do the maximum" to keep hold of Lukaku, but without Champions League football that is looking increasingly unlikely.
The Belgian has scored 83 goals in 157 games in all competitions for the Merseysiders since joining them, initially on-loan, back in 2013/14.