The Blues are reportedly eyeing a deal for the former Aston Villa defender now he has recovered from injury.
The Holland international left Villa at the end of last season after turning down a new deal at the club in the summer.
He has as yet failed to find a new club though, with him only having recently recovered from surgery after tearing his medial meniscus.
That has allegedly alerted Everton, who are considering the idea of offering the defender a deal to bolster their defensive ranks this season.
The Blues only have three senior central defenders in their squad, John Stones, Phil Jagielka and Ramiro Funes Mori, and Vlaar would give manager Roberto Martinez further options to choose from.
He has relied of youth this season in both full back positions, and while that has worked, further reinforcements would be a welcome boost.
Given Vlaar’s Premier League experience, and his availability on a free, a move would make sense for the Toffees.
However, they are not the only side interested in his services, with AC Milan an Inter Milan both keen, while there are also options in Germany and Turkey.