Sam Allardyce's side are now looking over their shoulder after a poor March that has seen them lose all of their Premier League fixtures.
Four wins in as many matches in February looked to have pushed West Ham towards survival, but since the turn of the month they have struggled, following defeats at Everton and Stoke City with a 2-0 home loss to Manchester United on Saturday.
West Ham now sit 14th in the table - just six points above the relegation zone - and were overtaken by Hull at the weekend by virtue of Steve Bruce's side's 2-0 win over West Brom.
"It is going to be tough. We've still got eight games left and we've got to put some points on the board," West Ham midfielder Mark Noble told the club's official website.
"Obviously it (is) a big game on Wednesday. Hull beat West Brom on Saturday so they are going to have confidence, but we need to play like we can do at home."
And manager Bruce believes one more triumph may be enough for the club to secure their position in next season's top flight.
Bruce told Hull's official website: "I've said all along that I thought 10 wins would be enough.
"Whatever it takes, we have to see it through but if we can get to ten wins with seven or eight games to play it means other teams have got to maybe win four and draw a couple which is very difficult."
Defender Joey O'Brien (dislocated shoulder) and striker Marco Borriello (calf) are set to miss out for the hosts.
Brady scored the only goal in Hull's 1-0 win in September's meeting between the two sides - just the fifth occasion they have met in Premier League history. West Ham and Hull have both won two of those clashes.
