Rovers saw their fourth round tie confirmed late on Monday evening as West Ham beat non-league Stockport County 1-0 to set up the meeting at the London Stadium on the weekend of January 23.
And they know who they have a chance of facing in the fifth round after draws took place for both rounds consecutively.
A mouthwatering trip to Manchester United or Liverpool awaits in the fifth round for the winner.
Rovers last faced Premier League opposition in the competition when they hosted Crystal Palace in the fifth round in 2019. That also happened to be the last time Rovers played a home tie in the FA Cup.
The last meeting between Rovers and West Ham came in March 2012 in the Championship with a James Coppinger goal earning a 1-1 draw at Upton Park.
Rovers’ home game against Rochdale, set for January 23, will now be rearranged due to the cup commitments.
Fourth round draw: Cheltenham Town v Manchester City; Bournemouth v Crawley Town; Swansea City v Nottingham Forest; Manchester United v Liverpool; Southampton/Shrewsbury v Arsenal; Barnsley v Norwich; Chorley v Wolves; Millwall v Bristol City; Brighton v Blackpool; Wycombe v Tottenham; Fulham v Burnley; Sheffield United v Plymouthl Chelsea v Luton; Stockport/West Ham v Doncaster; Brentford v Leicester; Everton v Sheffield Wednesday.
Fifth round draw: Fulham/Burnley v Bournemouth/Crawley Town; Manchester United/Liverpool v Stockport/West Ham or Doncaster; Sheffield United/Plymouth v Millwall/Bristol City; Chorley/Wolves v Southampton/Shrewsbury or Arsenal; Barnsley/Norwich v Chelsea/Luton Town; Everton/Sheffield Wednesday v Wycombe/Tottenham; Swansea City/Nottingham Forest v Cheltenham Town/Manchester City; Brentford/Leicester v Brighton/Blackpool