Munster and Leinster, both also past winners of the trophy, top their respective pools, while Cardiff Blues - the top-placed Welsh region - are only two points shy of their pool leaders, reigning champions Toulon.
The Irish provinces are faring well in the RaboDirect PRO12 as well, with three of the four play-off places taken up by them, Munster pulling out a four-point lead at the top of the table as the halfway point of the season approaches.
They are in action at Musgrave Park on Saturday evening when they face the Scarlets, the Welsh region having won at this venue the last time they visited.
The round starts off on Friday night with the remaining three teams currently in the play-off zone - Leinster, Glasgow Warriors and Ulster - all in action.
Second-placed Leinster travel to Murrayfield buoyed by the fact they have won their last five contests with Edinburgh, while in Glasgow, Benetton Treviso are the visitors.
Having led in the early part of the season the Warriors now reside in third place in the table, level on points with Ulster and need a win to keep their season on track.
The remaining top-four team, Ulster, will be looking to maintain their near perfect record against Italian teams when Zebre run out at Ravenhill.
Like Munster, Connacht are in action on Saturday evening, welcoming the Newport Gwent Dragons to the Sportsground. Pat Lam's men are chasing their first league victory since the opening round of the season when they beat Zebre at home.
RABODIRECT PRO12 - ROUND 10 FIXTURES:
Friday, December 20 -
ULSTER (4th) v Zebre (11th), Ravenhill, 7.05pm (live BBC 2 Northern Ireland)
Cardiff Blues (9th) v Ospreys (5th), Arms Park, 7.05pm (live BBC 2 Wales)
Glasgow Warriors (3rd) v Benetton Treviso (10th), Scotstoun Stadium, 7.35pm
Edinburgh (8th) v LEINSTER (2nd), Murrayfield, 7.35pm (live RTÉ Two/BBC ALBA)
Saturday, December 21 -
CONNACHT (12th) v Newport Gwent Dragons (7th), the Sportsground, 5pm
MUNSTER (1st) v Scarlets (6th), Musgrave Park, 7.15pm (live TG4/S4C)