Both Moyes and Bilic are having a difficult period at their respective clubs, with results not helping matters, the pressure is mounting as club owners are already demading more.
Moyes met with Sunderland’s owner Ellis Short and chief executive Martin Bain in London over the bank holiday weekend for a scheduled catch-up following the club’s confirmed relegation status from the Premier League.
Moyes, joined the Black cats on a four-year deal last July, remains undecided whether he will continue as manager in Championship next season.
Meanwhile, Bilic has suffered a disappointing second term at West Ham after leading them to seventh position last year.
The Hammers have struggled with the move to the London Stadium and the Dimitri Payet fiasco but were also let down by a poor recruitment process last summer.
And according to the Guardian Bilic has to impress in his final two home games of the season to save his job.
West Ham face Tottenham and Liverpool before playing Burnley away on the final day.
They still need three points to completely stave off the possibility of relegation.