According to talkSPORT the Hammers are thinking about replacing the 50-year-old manager with Bilic, 57, if owner David Sullivan decides to sack Potter.
Under Potter - who took over from Julen Lopetegui as head coach in January - West Ham have lost three of their first four games in the Premier League, and have so far conceeded a total of 11 goals this season.
West Ham are currently sat in 18th place, and are facing relegation.
Bilic managed West Ham from 2015 to 2017, and took the London side to seventh place in his first season at the club.
Nuno Espirito Santo and Sean Dyche are also reportedly in the running to become manager for the Hammers if the board decides to sack Potter.
West Ham’s poor start to the season has led to some fans calling for major change at the club, with some also planning to boycott Saturday’s (20.09.25) game with Crystal Palace.
After learning of the protest, the board released a statement, in which it admitted “nobody at the club is satisfied” with the current performance of the Hammers.
The board said: “First, we accept that results and performances on the pitch over the past two seasons have not met the standards we set for ourselves.
“Nobody at the Club is satisfied with that and the Board of Directors have spent a great deal of time looking at the decisions that have been made across the football operation, in order to inform an improved strategy going forward.
“Our focus now is firmly on the future and building a team that can once again compete consistently in domestic competitions and in Europe.
“We have a strong platform from which to continue that quest, in that we are entering our 14th consecutive season in the Premier League – our longest unbroken top-flight run in the modern era.”
Ahead of welcoming Crystal Palace to the London Stadium, Potter admitted the Hammers “have to focus on ourselves” and need to have time to “build” and “develop”.
He said in a post to the official West Ham site: “When you have those results, clearly they’re doing a lot right, as FA Cup winners into Europe.
“I think they’ve done a fantastic job in terms of how they’ve built that project. Under the coach and the board, they’ve worked together.
“So, yeah, they’ve got lots of good players and clearly know what they’re doing in and out of possession, in attack and defence. They’re solid.
“But like any team, nobody’s perfect. We have to focus on ourselves first and foremost and then look to see how we can attack and how we can defend to make it a problem for them as well.”
