Gary Neville believes there are still question marks about whether Romelu Lukaku is capable of performing on the biggest occasions.
The Belgium international has been heavily linked with a move to the Premier League leaders at the end of the 2016-17 season.
Chelsea manager Antonio Conte is thought to be keen to sign a top striker to replace Diego Costa ahead of the Spain international’s rumoured move to China.
Lukaku is the Premier League’s leading goal-scorer in the current campaign after a return of 24 goals in 33 games in the English top flight.
However, the Belgian centre-forward has failed to score against Arsenal, Chelsea, Liverpool and Manchester United this season.
Lukaku has faced criticism of his performances in big Premier League games since his move to Goodison Park from Chelsea back in 2013.
And Neville warned Chelsea that there is still a question mark lingering over Lukaku in terms of his big-game temperament.
“The question mark and frustration with Lukaku is does he do it in the big games? That won’t go away until he moves to a big club and starts delivering,” said Neville, speaking to the Gary Neville podcast.
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Lukaku moved to Everton from Chelsea on loan in 2013 before completing a club-record move 12 months later.