The former Liverpool defender believes that Everton need to start competing for the Champions League places, or they could lose the Belgium international striker in the summer of 2018.
Carragher has also suggested that the 23-year-old could leave the Merseyside outfit in the summer of 2017.
“Having spoken to Rom — I'm on first-name terms with him now! — there is no doubt he sees himself as potentially one of the top strikers in the Champions League and he wants to be there,” Carragher wrote in The Daily Mail.
“If Everton don't get into that competition in the next 18 months, sadly that will be the end of him at Goodison Park. He may even leave this summer.”
Lukaku is one of the best strikers in the Premier League and could end up as the top scorer in the league this season.
The former Chelsea striker has found the net 21 times in the league so far this campaign, two more than Tottenham Hotspur’s Harry Kane.
Given the 23-year-old’s potential and form for Everton, it does make sense for him to crave Champions League football and play against the best teams in the world.
While Everton fans would be disappointed if Lukaku left in the summer, they should at least be pleased that he is doing all he can to make this season a success for Ronald Koeman’s side.