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The Hammers have taken up the option of extending Antonio's deal by a year and adding in another option for a further year, meaning he could stay at the club until 2025.
The striker's new deal was sealed two months ago but emerged this week, while Moyes added that other players have also extended their contracts but would not name them.
Lukasz Fabianski, whose deal runs out this summer, has been in talks over a new deal, while Vladimir Coufal agreed terms earlier this year, though neither have been confirmed by the club.
Full-backs Ben Johnson and Aaron Cresswell are two other players West Ham would like to tie down further.
“We've actually extended one or two contracts behind the scenes and we did Michail's contract two months ago,” said Moyes.
“We've done another couple of players and we're going about our business quietly and trying to do things correctly.
“We've got a few more who have signed contracts and I'm sure the club will announce it at the right time.
“We are changing, trying not to do our business in public. We're trying to do our business in the correct fashion if we can, getting around one or two players at different times and extend their contracts.”
West Ham have often been surrounded by noise and speculation during transfer windows and there is now a push from Moyes, and figures in the boardroom, to work in a more private manner.