Tigers topped Pool 3 after earning a bonus point at the Ospreys on Saturday, and were paired with old rivals Bath when the West Countrymen drew 3-3 with Toulouse at The Recreation Ground 24 hours later.
The pair last clashed in Europe at the same stage of the tournament in 2006 when Bath triumphed 15-12 and the sides have already met three times this season, with each winning the Guinness Premiership fixture on home ground andTigers winning an EDF Energy Cup tie at The Rec.
The European quarter-final ties are scheduled for the weekend of April 10-12. Tournament organisers ERC will discuss the schedule with broadcasters before revealing kick-off dates and times.
Ticket details will follow once the fixture has been confirmed.
Quarter-final line-up: Cardiff Blues v Toulouse, Munster v Ospreys, Harlequins v Leinster, Leicester Tigers v Bath Rugby.