Edinburgh themselves need a bonus point win at the RDS, and hope that other results go their way, to stand any chance of securing fourth place, while one match point will give Leinster the luxury of a home semi-final tie.
Round 18 opens on Friday night with two of the top four teams in action in Wales - the second-placed Ospreys hosting the Newport Gwent Dragons, and Glasgow Warriors, currently lying third in the table, visiting the Scarlets.
With just one match point separating them, any slip-up by either team could give the other the opportunity of claiming home advantage in the Magners League semi-finals.
Also on Friday, Ulster face Connacht at Ravenhill, and only an unprecedented scoreline would give Connacht any mathematical chance of overtaking their provincial rivals in the table.
This round brings to a conclusion the league stage of this season's competition, and the top four teams will go forward to the inaugural Magners League semi-finals (May 14-15).
MAGNERS LEAGUE - ROUND 18 FIXTURES:
Friday, May 7 -
Ospreys v Newport Gwent Dragons, Liberty Stadium, 7.05pm (live Setanta Sports 1/BBC Wales)
Scarlets v Glasgow Warriors, Parc y Scarlets, 7.05pm
ULSTER v CONNACHT, Ravenhill, 7.30pm (live Setanta Sports Ireland)
Sunday, May 9 -
Cardiff Blues v MUNSTER, Cardiff City Stadium, 6.15pm (live Setanta Sports 1/S4C)
LEINSTER v Edinburgh, the RDS, 6.15pm (live Setanta Sports Ireland)