The fifth-tier side secured an extra-time win in their second-round fixture against Yeovil Town to book their place in this round.
Both clubs have one win, one loss and two draws in their last four outings.
Stockport County vs West Ham United Head-to-Head
The two clubs have locked horns 14 times across all competitions. This will be their first meetings in the 21st century.
The Hammers have seven wins to their name while The Hatters have won three games in this fixture. Four games have ended in a stalemate.
There have been three encounters in the FA Cup between these two sides. Each team have secured one win apiece and one game has ended in a draw.
They last met in the League Cup in 1996, when the hosts recorded a 2-1 win.
Stockport County form guide in the National League: D-W-D-L-L
West Ham United form guide in the Premier League: W-D-D-L-D
Stockport County vs West Ham United Team News
The hosts have reported a clean bill of health heading into the fixture. Midfielder Harvey Gilmour's availability is in doubt, according to the club.
Manager Jim Gannon has not named defender Ash Palmer in the squad since his red card on 22 December and his involvement in this cup tie remains in doubt.
Striker Nyal Bell has been recalled from his loan spell at FC Halifax Town and is in contention to start the game.
Injured: Harvey Gilmour
Doubtful: Ash Palmer
West Ham United
West Ham United will be without the services of Arthur Masuaku, who is recovering after a successful knee operation.
Defender Ryan Fredericks tested positive for COVID-19 last week and remains in self-isolation. Goalkeeper Łukasz Fabiański will play no part in the game.
The team have released Sebastian Haller and Robert Snodgrass in the ongoing transfer window.
Injured: Arthur Masuaku, Łukasz Fabiański, Ryan Fredericks
Stockport County vs West Ham United Predicted XI
Stockport County Predicted XI (4-4-2): Ben Hinchliffe; Liam Hogan, Jordan Keane, Jamie Stott, James Jennings; Adam Thomas, Ryan Croasdale, John Rooney, Mark Kitching; Connor Jennings, Alex Reid
West Ham United Predicted XI (3-4-3): Darren Randolph; Fabian Balbuena, Angelo Ogbonna, Issa Diop; Vladimir Coufal, Declan Rice, Thomas Soucek, Aaron Cresswell; Jarrod Bowen, Michail Antonio, Pablo Fornals
Stockport County vs West Ham United Prediction
Though both clubs are unbeaten in their last three games, the visitors are the clear favorites in this fixture.
The sheer difference in the quality of players in the starting XI will be a decisive factor in the game.
We predict a win for visiting West Ham United in this FA Cup clash.
Prediction: Stockport County 1-2 West Ham United.Published 09 Jan 2021, 13:29 IST