The English and French clubs are at loggerheads with their rivals from Wales, Scotland, Ireland and Italy over the future shape of European rugby. Talks have reached a stalemate and if no agreement can be put in place for the 2014-15 season, then there will be no Heineken Cup and no Amlin Challenge Cup.
"You cannot have a product that is this good and not continue it," said Schmidt, who guided Leinster to successive Heineken Cup triumphs.
"The Premiership clubs are pretty well represented this year. Leicester, Saracens and Harlequins all have great shots.
"That inevitably will get enthusiasm and clubs will want to do what their supporters want to see. Therefore, with competitions like this, I just don't think people are going to allow to let it slip.
"I think one of the options that have been discussed will come to be and hopefully it will be inclusive of the whole of Europe and we will continue what has been a fantastic tradition over the last 15 years."
The English and French clubs want to change the format of the Heineken Cup and force every club to qualify, ending the right of automatic entry currently enjoyed by Scotland and Italy. The plan proposed by Premiership Rugby would reduce the Heineken Cup to 20 teams with four dropping into a strengthened Amlin Challenge Cup.
But the Rabodirect PRO12 clubs have dug their heels in, arguing the Heineken Cup has to be representative of the whole of Europe and the only way to ensure that is by guaranteeing entry. After four rounds of talks, the gap between the two sides remains unbridgeable and there are no further meetings planned.
Although the English clubs maintain that Europe is their priority, they have received approaches about potential alternative competitions.
But for Schmidt a dramatic weekend of quarter-finals in the Heineken Cup and the Amlin Challenge Cup will start to focus the minds of those in the corridors of power.
- Sports & Recreation
- Heineken Cup