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Adrian is in contention to feature after impressing against Manchester City last weekend, stepping in when Hart was ineligible to face his parent club.
With Hart also under pressure for his England number one spot from Jordan Pickford and Jack Butland, losing his club place could leave his Russia 2018 hopes in tatters.
“I’ll keep my team until tomorrow,” said Moyes. “But I have made a decision in my own mind.”
As for whether he had discussed that decision with Hart, Moyes added: “I would always try to speak to the players. There are some occasions you should speak to them and others there is no need to.
“It is a good problem for West Ham. I don’t know if it is a good problem going into the World Cup. I would like those problems in a few other positions. I am happy having the two of them.”
West Ham skipper Mark Noble is another casualty of Moyes’s arrival at the London Stadium.
The long-serving midfielder was a favourite of previous manager Slaven Bilic but has not made an appearance since the Scot took charge and was not even in the squad at City.
“Mark is really influential, he’s great around the club,” said Moyes. “But he is not guaranteed. No one is guaranteed. We have to find a way of winning. I want to pick the players who are in form.”
Champions Chelsea make the trip from west to east London lying in third and looking to move level on points with Manchester United, who face leaders City on Sunday.
“I’m not a Chelsea expert but how they played last year was fantastic,” said Moyes. “A slow start to the season might have caught them out a little bit but on their day they are a match for anyone.”
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