Everton manager Ronald Koeman is a keen admirer of fellow Dutchman De Vrij, having coached him at Feyenoord.
The centre-back is out of contract next summer and Lazio have failed to convince him to sign fresh terms.
Inter Milan have also been tracking the 25-year-old but the Daily Star Sunday claim Everton’s biggest rivals for his signature are in fact Chelsea.
According to the report, the Toffees are willing to spend the £30million required to snap up the Netherlands international.
But even the prospect of playing under Dutchman Koeman may not be enough to convince De Vrij to move to Merseyside.
According to the report, Chelsea is a more appetising prospect for the ex-Feyenoord player, who would find it hard to reject the chance to play for the Stamford Bridge club.
Chelsea and Everton reportedly want to sign Stefan de Vrij (left)
De Vrij's contract at Lazio expires in 2018
It is claimed De Vrij (left) could be tempted by a move to Chelsea
Ronald Koeman (right) used to manage De Vrij when in charge of Feyenoord
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Chelsea can all-but guarantee Champions League football for next season as they close in on the Premier League title in manager Antonio Conte’s first season in charge.
Everton, meanwhile, sit seventh in the table but are hoping to enter the race for a Champions League spot and sit just six points off the top four.