Rovers have been drawn away to Championship rivals QPR in the third round of the FA Cup.
The tie will take place at Loftus Road on the weekend of the 7th/8th January 2017.
It was honours even in the league meeting between Rovers and Rangers at Loftus Road earlier this season, as a Sam Gallagher header cancelled out Tjaronn Chery's free-kick back in September.
The last time the two teams met in the FA Cup was also at the third round stage, when Rovers ran out 1-0 winners at Ewood Park in January 2011.
Junior Hoilett, who would later join the Hoops, scored the only goal of the game, whilst Rovers skipper Jason Lowe made his debut for the club.
The only other FA Cup clash between the clubs was also a third round tie at Ewood Park and again Rovers advanced to the fourth round, winning 3-0 in January 2006 thanks to a superb Craig Bellamy brace and a goal from Andy Todd.
Third round draw in full:
Ipswich Town v Lincoln City/Oldham Athletic
Barrow v Rochdale
Manchester United v Reading
Hull City v Swansea City
Sunderland v Burnley
Queens Park Rangers v Rovers
Millwall v AFC Bournemouth
West Ham United v Manchester City
Brighton & Hove Albion v MK Dons/Charlton Athletic
Blackpool v Barnsley
Wigan Athletic v Nottingham Forest
Birmingham City v Newcastle United
Chelsea v Peterborough United/Notts County
Middlesbrough v Sheffield Wednesday
West Bromwich Albion v Derby County
Everton v Leicester City
Liverpool v Newport County/Plymouth Argyle
Wycombe Wanderers v Stourbridge/Northampton Town
Watford v Burton Albion
Preston North End v Arsenal
Cardiff City v Fulham
Stoke City v Wolverhampton Wanderers
Cambridge United v Leeds United
Bristol City v Fleetwood Town/Shrewsbury Town
Huddersfield Town v Port Vale
Tottenham Hotspur v Aston Villa
Brentford v FC Halifax Town/Eastleigh
Bolton Wanderers v Crystal Palace
Norwich City v Southampton
Sutton United v AFC Wimbledon
Accrington Stanley v Luton Town
Rotherham United v Oxford United/Macclesfield Town