The Hammers come to Molineux for the second round tie having opened their Premier League season with a 3-0 defeat to newly promoted Sunderland and a 5-1 thrashing at the hands of London rivals Chelsea.
They sit bottom of the table and face a Wolves team that has also lost their first two matches - as the only two clubs not to pick up a point yet this season face off in the Carabao Cup.
But in contrast to Wolves, at West Ham the manager is already under some pressure.
Potter's position is being scrutinised by fans, with many of them already calling on chairman David Sullivan to make a change, despite reports in national media suggesting that Sullivan intends to give Potter some more time and understands his frustration at a lack of signings.
The Hammers chairman is often patient with managers and tends to avoid sacking them during a season - although he bucked that trend in January when he sacked former Wolves boss Julen Lopetegui.
Potter may well be given more time, but he still faces an uncertain period where a result against Wolves, even in the cup, would be welcomed.
He will have to find the right balance in his team selection, to give players an opportunity to play but also give his side the best possible chance of winning the game.
Alphonse Areola is likely to come in between the sticks, while youngster Freddie Potts could play in midfield.
It also remains to be seen if Max Kilman - who made a £40million move to West Ham from Wolves in 2024 - will play against his old team.
The defender has come under criticism from many West Ham fans for his performances.