Zouma suffered a serious knee injury in 2016 and after returning to fitness, he was unable to break back into the team on a regular basis.
The French defender had to watch on as Cesar Azpilicueta, Gary Cahill, David Luiz performed impressively on the way to winning the Premier League.
Last week Chelsea completed the signing of Antonio Rudiger from Roma which is likely to mean even less minutes for Zouma.
A number of clubs have been interested in taking Zouma on loan.
And French newspaper L'Equipe say he will play under Mark Hughes at the Bet365 stadium next season.
Chelsea predicted team for 2017/18 Sat, July 15, 2017
Express Sport predicts how the Chelsea squad could look on the opening day of the 2017/18 season
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How might the Chelsea starting XI and bench look in 2017/18?
Kurt Zouma will join Stoke on Monday
The report says Zouma will extend his contract for two more seasons, until June 2021 and sign for Stoke on a season-long loan.
Earlier this week, Hughes made clear he wanted to sign Zouma saying: "There is genuine interest.
"We'd like to make it happen if we can.
"The boy himself has to make a decision. We are one of many interested parties but we're very hopeful.
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"We're still doing a number of deals."