Leicester will host PSV Eindhoven in the first leg of the quarter-final in the Europa Conference League.
Brendan Rodgers' men qualified 3-2 on aggregate after losing 2-1 to Rennes on Thursday, and find themselves in a tie with one of the stronger sides left in the competition.
Jose Mourinho may not have been too pleased to see his Roma side drawn against Norwegian side Bodo Glimt.
The two sides were in the same Conference League group, and while Roma only managed a 2-2 draw at home, they were stunned 6-1 by Bodo/Glimt in Norway.
However, Roma have bounced back since that defeat and will hope to have the services of their talismanic striker Tammy Abraham.
The former Chelsea striker has scored 21 goals in all competitions for Roma this season, including seven goals in eight Europa Conference League games.
Should both sides go through, Leicester and Roma will meet each other in the semi-finals, meaning only one of Rodgers or Mourinho will make it to this year's final.
In the other fixtures, Feyenoord will host Slavia Prague, another fixture with two teams who were in the same group, and Marseille are at home to Greek side Paok.
The quarter-final first and second legs will be played on April 7 and April 14 respectively.
The final will be played in Tirana, Albania on May 25.