La Rochelle, who are second in the Top 14 league, qualified for the last eight as one of the best three pool runners-up.
Edinburgh, who won Pool Five, played their first game of the season at Myreside - their home for the second half of the campaign - on Friday.
But they may opt to shift the quarter-final back to Murrayfield.
Myreside can hold around 5,500 spectators, while Scotland's national stadium seats more than 67,000.
The last-eight fixtures take place on the weekend of 31 March-2 April.
La Rochelle finished second in Pool One behind Gloucester, ending their group campaign with a 31-8 home win over Benetton Treviso, who had led until the 57th minute in France.
Edinburgh secured a home quarter-final with a 49-3 win over Romanian outfit Timisoara Saracens.
Edinburgh will host French outfit La Rochelle in the European Challenge Cup quarter-finals.