The Brazil Serie A outfit last reigned in South America in 1995, but made the final as recently as 2007.
Gremio's two-leg tie with their Argentine opponents is squeezed into a packed schedule for both clubs, who will have to manage their squad around their respective domestic campaigns.
San Lorenzo have proven to be a tough team to break down at home in the Copa this campaign, as they have two wins and a draw from their three home fixtures.
The only side to score at the Estadio Pedro Bidegain was Union Espanola, who hit a late equaliser to earn a 1-1 draw.
However, Gremio can lay claim to a sensational away record in the tournament, similarly shipping just one goal in three trips and claiming seven points from them.
It is the first meeting between the two clubs.
Other last-16 ties beginning on Wednesday and Thursday this week all have either an Argentine or Brazilian flavour.
Velez Sarsfield are on the road at Paraguay's Nacional Asuncion, with the Argentine outfit out of form after consecutive domestic losses.
Asuncion are strangely out of scoring form in the Division Profesional, without a goal in 199 minutes domestically, but put three in the back of the net last time out in the Copa against Santa Fe.
Also on Wednesday, Atletico Mineiro of Brazil are on the road at Colombia's Atletico Nacional.
Finally on Thursday, Argentine club Arsenal are at home to Chilean side Union Espanola, who have either won or lost their past nine matches in all competitions.
Arsenal, meanwhile, have just one win from five in all comps, although that victory came in the Copa over Santos Laguna 3-0.
