One of those teams, Ulster, will host Joe Schmidt's men at Ravenhill on Friday night. Any points they can pick up their game against Leinster will be welcomed as they face a trip to the reigning champions, Munster, in the final round.
The second-placed Ospreys are also in action on Friday in an all-Welsh affair against the Newport Gwent Dragons, before facing a final round trip to Aironi. One more win, or less should other results go their way, will secure the Ospreys a top four finish.
The Scarlets host Munster at Parc y Scarlets on Saturday in what is a 'must win' game for both sides if they wish to further their ambitions in the knockout stages.
Meanwhile, the remaining team still in with a chance of making it into the play-offs, fourth-placed Glasgow Warriors, are in action on Sunday travelling to Benetton Treviso.
At this stage of the season any points dropped can make the difference between having a chance for a shot at the title, or the season being over for another year.
With the margins so tight, it is still anyone's guess who will be joining Leinster in the knockout stages of the RaboDirect PRO12. The eyes will certainly be on the prize as round 21 unfolds.
RABODIRECT PRO12 - ROUND 21 FIXTURES:
Friday, April 20 -
Ospreys v Newport Gwent Dragons, Liberty Stadium, 7.05pm (live BBC 2 Wales)
ULSTER v LEINSTER, Ravenhill, 7.05pm (live BBC 2 Northern Ireland/RTÉ Two)
Saturday, April 21 -
CONNACHT v Aironi Rugby, the Sportsground, 5pm
Scarlets v MUNSTER, Parc y Scarlets, 6.30pm (live TG4/S4C)
Sunday, April 22 -
Cardiff Blues v Edinburgh, Cardiff City Stadium, 2.05pm (live BBC 2 Wales)
Benetton Treviso v Glasgow Warriors, Stadio di Monigo, 3.05pm local time (live Rai Sport 2)