The Hammers will enter the match off the back of four straight wins, while Doncaster have been victorious in their last three, including a 1-0 success at Blackburn Rovers in the third round of the FA Cup.
West Ham's form in recent weeks, and for the majority of the 2020-21 campaign, has certainly given their supporters reasons to be optimistic, and the Hammers will be eyeing a spot in the fifth round of the FA Cup when they welcome League One opposition to the English capital.
David Moyes's side were far from their best in the third round of the competition, needing a late goal from Craig Dawson to overcome Stockport County, but they have also been victorious twice since then in the Premier League, beating Burnley and West Bromwich Albion in quick succession.
West Ham are now up to seventh in the Premier League table and will be looking to make it four league victories in a row when they travel to Crystal Palace for a London derby on January 26.
However, the Hammers must first focus on the FA Cup - a competition that they have won on three previous occasions, the last of which came in 1980, beating Arsenal in the final.
The capital giants also reached the 2006 final - losing to Liverpool - and they will face either the reigning Premier League champions or Manchester United in the next round of the tournament with a victory here.
Doncaster, meanwhile, will also enter this match in strong form, winning their last three matches against Blackburn, Swindon Town and Rochdale.
Donny will be the underdogs heading into this weekend's contest, but they are enjoying a strong season to date, picking up 39 points from 20 matches to occupy fourth position in League One.
Doncaster have not actually beaten West Ham in any competition since a 3-0 success in Division Two back in 1956, but they did hold the Hammers to a 1-1 draw when the pair last locked horns in the Championship during the 2011-12 campaign.
West Ham United FA Cup form: LWLWLW
West Ham United form (all competitions): DDWWWW
Doncaster Rovers FA Cup form: DWLWWW
Doncaster Rovers form (all competitions): WWLWWW
West Ham will again be without the services of Arthur Masuaku due to a long-term knee problem, but the Hammers are otherwise in good shape heading into the contest.
As for Doncaster, Moore is expected to name a similar side to the one that started the previous round against Blackburn, with Richards again featuring in an advanced area.
West Ham United possible starting lineup:
Randolph; Fredericks, Dawson, Balbuena, Johnson; Rice, Noble; Bowen, Fornals, Benrahma; Yarmolenko
Doncaster Rovers possible starting lineup:
Balcombe; Wright, Anderson, Butler, John; Halliday, James; Okenabirhie, Richards, Simoes; John-Jules
We say: West Ham United 2-1 Doncaster Rovers
Doncaster's recent form must be respected, and there is every reason to believe that the visitors will prove tricky opposition for West Ham. The Hammers are on a bit of a roll at the moment, though, and we expect them to advance to the fifth round of the competition courtesy of a 2-1 success.