Moyes has managed to steer West Ham away from the threat of relegation this season and they have reached their first European final in close to five decades.
There have been suggestions that West Ham are considering replacing the Scot this summer despite him having a year left on his contract.
West Ham did carry out checks on names such as Paulo Fonseca, Brendan Rodgers, Graham Potter, Marco Silva and Ange Postecoglou as a potential replacement for Moyes.
But it has been claimed that the Hammers are now unlikely to try and find a new manager in the summer.
The former Manchester United boss is now expected to be allowed to see out his contract next season.
Despite his team’s struggles this season, his relationship with the board never soured and the club have immense respect for what he has achieved at West Ham.
A final decision has not been made and the club will hold talks with Moyes at the end of the season.
But it now seems likely that Moyes will be in the West Ham dugout on the first day of the 2023/24 Premier League season.