The match is heading for a sell-out - the first at the DAM Health Stadium - and both teams know that a win would guarantee them a place in the United Rugby Championship play-offs.
In reality, the match is part of the penultimate round of regular season fixtures and Edinburgh still have an inter-city derby against Glasgow Warriors at Murrayfield on May 21, while Ulster finish up at home to the Sharks on the night before.
Both sides have been flying high for most of the season but they have slipped out of the top four, the all-important criterion for securing a home tie in the quarter-finals.
Finishing between fifth and eighth will secure a place in the play-offs but could mean a last-eight tie in South Africa.
With only four points separating Stormers in second place and Bulls in eighth, it’s all up for grabs, and ninth-placed Scarlets haven’t given up hope of forcing their way into the play-off positions.
“You look at how tight the league is - there’s not much between ninth and second so we know that these two games are equivalent to knockout games because they will determine how things will go after that,” said Grant Gilchrist, the Edinburgh captain.
“We know how big playing Ulster is and we know we need to win one of the last two to get into the last eight and if we want to play at home then we have to win them both.
“We would love to play a home quarter-final here. That would be a huge statement by the club but it would also give us the best opportunity to go further in the competition.”
Edinburgh, who are unbeaten at home in competitive matches this season, are currently seventh, two points behind fifth-placed Ulster.
There is a sense around the club that this could be the season when they finally win a major honour, something that has eluded them in the professional era. For the long-serving Gilchrist, it would be the culmination of years of hard graft.
“It would mean so much to me,” said the lock. “This place, this group of players, the club has been a huge part of my life. It would be the highest and best moment I could have on a rugby pitch if I could do that.”
Edinburgh are also chasing silverware in Europe and host Wasps in the Challenge Cup quarter-finals on Saturday week. Gilchrist believes the depth of the current squad means they can fight on two fronts but knows they will need to step up a notch after the lukewarm performance against Zebre last week.
“We have two home games in the leagues and a home quarter-final in Europe,” he said. “We can control our own destiny, but if we are slightly off, as we found out at the weekend, it can quickly unravel.
“We are going to have to be better against Ulster and then better again against Glasgow and better against Wasps. But if we can keep doing that, keep growing as a squad, then we will back ourselves and look forward to it.”