Tigers are two points behind the French heavyweights and Pool 2 leaders, with only the group winners guaranteed a quarter-final place.
Victory for Leicester would take them through, albeit to then face a potential last-eight clash away against European title contenders like Clermont Auvergne or Toulon.
“We have set the occasion up for next week. That was our aim, and it should be a classic,” said Tigers rugby director Cockerill, following his team’s 15-15 Liberty Stadium draw against the Ospreys.
“We are disappointed that we didn’t win today and won’t have a chance to be at home in the quarters, but we are set up for a winner-takes-all with Toulouse at Welford Road.
“If we get past Toulouse, and that’s an if at this point, then we are in with a fighting chance.”
Ospreys substitute Jonathan Spratt’s 77th-minute try denied Leicester victory in an absorbing tussle.
The visitors looked to have done enough through quickfire second-half touchdowns from scrum-half Ben Youngs and wing Niall Morris, after they trailed 10-3 for much of the contest after Ospreys posted a 34th-minute Joe Bearman try.
Dan Biggar and his opposite number, Toby Flood, each kicked a conversion and penalty, but the Ospreys would have won had Biggar not missed four penalties – three of them either hit the post or bar – and a late conversion.
A bonus-point 35-14 win over Benetton Treviso saw four-time Heineken Cup winners Toulouse leapfrog the Tigers at the pool summit.
Tobias Botes’ early penalty gave Treviso the lead but after Gary Botha got over in the sixth minute, Toulouse would not look back.
Tommaso Benvenuti dotted down four minutes later to level the scores but further tries from Patricio Albacete, Vincent Clerc and Florian Fritz sent the hosts well clear.
Yohan Huget got over in the 80th minute to rubber-stamp a comfortable win.
The French club are now guaranteed a quarter-final place if they can avoid defeat at Welford Road next Sunday.