Frank Lampard wants to bolster his defensive options after seeing Yerry Mina and Ben Godfrey leave the pitch due to injuries in their season opener against Chelsea.
Godfrey suffered a fractured fibula while Mina has an ankle problem and the timeframe of their absences is unknown.
The Toffees have agreed to take Coady on an initial loan deal with an option to make the deal permanent for around £12 million plus add-ons.
They will now negotiate on personal terms with the representatives of the Merseyside-born centre-back.
Despite being fit enough to start, the former Huddersfield Town defender was an unused substitute in Wolves’ 2-1 defeat against Leeds United at Elland Road.
It was the first time the Wolves captain has been left out of a game without being injured since April 2017, which points to the defender being one step away from Goodison Park.
Following the arrival of Nathan Collins from Burnley, the England international wants assurances of regular playing time, with one eye on the coming World Cup in Qatar.
Coady came up through the youth ranks at Liverpool but only made two senior appearances for the Reds before being shipped off to Huddersfield.
After 48 appearances for the Terriers, the Englishman moved to Molineux in 2015. He has been a mainstay in the Wolves defence ever since.
Coady has made 317 appearances during his seven-year stay, contributing seven goals and seven assists while becoming the club captain and a fan favourite.
He has plenty of experience playing in a back three and would slot in seamlessly with Mason Holgate and James Tarkowski in Lampard’s set-up in place of the injured duo.
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