Moyes is out of contract at the London Stadium next summer and West Ham have not decided whether to offer him fresh terms.
Despite Moyes leading the club back into Europe and also to silverware in the shape of the Europa Conference League, the Hammers could let him go.
And the club have already done some initial groundwork into who could replace the Scot in the summer.
West Ham will start to assess whether they want to keep Moyes when they move into 2024.
Moyes currently has West Ham sitting in ninth spot in the Premier League, while they are also through to the last 16 of the Europa League.
The former Manchester United boss has been hailed for his work at the London Stadium, but it may not be enough to see West Ham look to keep him.
Moyes started a second spell as West Ham boss at the end of 2019 and has a win percentage that is over 47 per cent.
