Harlequins are one of eight Premiership One clubs drawn away, including the holders Leicester and 10-times winners Bath, but they will have no fears about travelling to Loftus Road, where they won in the league last season.
London Scottish will have to sort out a fixture clash with Richmond, their co-tenants at the Athletic Ground, who have been drawn against Doncaster.
National League One side Doncaster - the equivalent of the fifth division - have come through all three rounds by beating Scunthorpe, Nottingham and Tynedale.
The other Yorkshire clubs are also away, with Wakefield at West Hartlepool and Rotherham at Bracknell.
The Premiership leaders, Newcastle, host Exeter, while Saracens will make the short journey across London to Blackheath.
There is an all-East Midlands Derby at Northampton, who host Bedford, while Gloucester, London Irish, Bristol and Sale from Premiership One are all on their travels.
TETLEY'S BITTER CUP Fourth round: Wasps v Harlequins; Moseley v Sale; Camberley v Newbury; Fylde v Rosslyn Park; Coventry v Leicester; Bracknell v Rotherham; Newcastle v Exeter; Blackheath v Saracens; Worcester v Bristol; Richmond v Doncaster; West Hartlepool v Wakefield; Rugby v Reading; Manchester v London Irish; London Scottish v Bath; Northampton v Bedford; London Welsh v Gloucester. Ties to be played 3 January 1998.
l Doddie Weir has been ruled out of Scotland's international with Australia on 22 November, despite continuing to play for his club, Newcastle, with a recurring back injury.Reuse content