Zouma, 23, spent last season on loan with Stoke City, making 34 Premier League appearances to confirm his fitness after a knee injury limited his opportunities at Chelsea.
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As it stands, Alderweireld and Maguire are considered too expensive, while Bayern Munich have knocked back a loan move for Boateng.
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Everton want to add further quality to their ranks following a hectic finale to the summer transfer window, with Zouma identified as a loan target.
"Capped twice by France, he lifted the League Cup under Jose Mourinho in 2015".
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Mourinho was the Chelsea manager when Zouma arrived in 2014, and he seemingly has a lot of belief in the Frenchman, although it's hard to see how he will boost his options in the short-term.
The Mirror believe Everton submitted a deal sheet that could go allow them to sign the France worldwide, despite the deal going beyond the 5pm deadline for Premier League clubs.
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According to The Times, Everton are now on the brink of completing a deal for the French defender.