Tigers currently top the Pool with a one point cushion over French champions Toulouse, who they host in the sixth round next week. Toulouse host Benetton Treviso in Round 5.
"The Ospreys are a top quality team with internationals all over the pitch. There is a huge amount at stake in the match and it also has the extra spice of being an Anglo-Welsh contest," said Tigers center Allen.
"We are in good shape at the moment, but we know we have two very difficult games left in our Pool against two very good teams. Getting out of our Pool will be massive for us.
"We've missed out in two of the last three seasons and, when the Pool draw was made, it was obvious we were in one of the 'Pools of Death'. We were bitterly disappointed to lose in Toulouse, especially after holding them in the first half-hour, and Benetton Treviso gave us two very hard games.
"Getting five points against the Ospreys at Welford Road was a huge bonus for us, but we are under no illusions as to how hard it is going to be for us at the Liberty Stadium.
"This weekend's game and the final match with Toulouse have been in the back of our minds for the last few weeks and there is a real air of excitement around the players at the moment. We have a huge opportunity to make the last eight, but we'll have to be at our best to make the most of it."