While the Hammers sit in 10th position in the top flight, fifth-tier Stockport hold fourth place in the National League standings.
Having collected 26 points from 17 Premier League matches this season, David Moyes will feel that he is well on his way to earning a long-term contract with West Ham.
However, the Scot is aware that an extended run in the FA Cup will strengthen his case, particularly with the club having reached just one final in four decades.
Nevertheless, Moyes will feel that this is an opportunity to hand chances to some of the club's fringe players as he contemplates his options in the transfer market.
With successive clean sheets being recorded at Southampton and Everton, there will be a high level of expectation that a third shutout in a row will come on Monday night.
Stockport, who are also on a three-match unbeaten run, will have other ideas as they bid to write another chapter in their cup history.
Almost 24 years have passed since County reached the semi-finals of the League Cup, a run which coincidentally saw West Ham defeated on their way to the last four.
Times have changed since they narrowly missed out on a place in the 1997 final, but Jim Gannon and his squad have put themselves in a position where they are challenging for promotion back to the EFL.
Stockport have reached this stage of the competition by recording victories over Chesterfield, Rochdale and Yeovil Town, the most recent win seeing them net two equalisers before sealing their progress in extra time.
Stockport County FA Cup form: WWW
Stockport County form (all competitions): LWLDWD
West Ham United form (all competitions): WDLDDW
Despite this game being West Ham's only fixture over a two-week period, Moyes is expected to make a number of changes to his team.
Michail Antonio is in contention for a recall in attack, although Moyes will take the forward's injury record into consideration before making a decision.
Rooney and forward Alex Reid have scored six of Stockport's nine goals in this season's competition.
Stockport County possible starting lineup:
Hinchliffe; Keane, Hogan, Palmer; Southam-Hales, Rooney, Maynard, Croasdale, Kitching; Reid, Jennings
West Ham United possible starting lineup:
Randolph, Johnson, Dawson, Diop, Cresswell; Noble, Rice; Yarmolenko, Lanzini, Benrahma; Antonio
We say: Stockport County 0-3 West Ham United
Despite the lack of home crowd, Stockport will fancy their chances when it comes to making things uncomfortable for their more illustrious opponents. However, we feel that an early goal will set West Ham on their way to a routine win in the North West.