Remarkably, Murray has never played at either Ravenhill or Donnybrook, but he hopes to correct part of that by coming off the bench in Belfast.
The fact that Ulster and Munster have won both of their opening games adds some early-season spice to this clash, but Murray does not see the first Irish derby of the season as a revenge mission for his side's Heineken Cup quarter-final loss to the northerners.
"It hasn't really been mentioned at all, but people obviously will remember that Ulster knocked us out. We played them a couple of weeks later after that," said the 23-year-old.
"It is in people's mind but I don't think it will play that big a part.
"It is a new season, with a new coach, a lot of new players -- it is a new beginning. I don't think we can dwell on the past unless we end up meeting them in the quarter-final of Europe again."
Murray is one of three returning Irish internationals available to new coach Rob Penney this weekend and, like Ronan O'Gara and Keith Earls, he will start on the bench, having sat out the victories over Edinburgh and Treviso.
"I am just itching to get back and be involved again. Hopefully I'll get off the bench this week and get a bit of a run out and get the cobwebs out. It has been a bit frustrating watching the lads the past few weeks, playing so well," he said.
"Rob has brought in a different style of play that the lads have adapted well to. You have seen glimpses of it the past few games.
"It is very promising, we are still getting to grips with it and finishing off little bits of it. I can't wait to get involved with it and see how I cope with that game plan."
Penney has made three changes to the side that defeated Treviso 19-6 at Thomond Park. Wian du Preez is rested, with Dave Kilcoyne coming in at loosehead, while on the other side of the scrum BJ Botha returns in place of Stephen Archer.
The return of Murray sees Peter Stringer drop to the Munster 'A' team, who play Ulster at Belfast Harlequins tomorrow. Also included in that 'A' side is Niall Ronan, who returns to the Munster colours for the first time since suffering a serious knee injury in January.
Meanwhile, Ireland's Grand Slam- winning scrum-half Tomas O'Leary has admitted that London Irish need to kickstart their English Premiership season with a win against Wasps this weekend.
"The first week was not acceptable," said the former Munster No 9, whose side have shipped 80 points in successive defeats to Saracens and Gloucester.
"Last weekend was an improvement but we didn't get the win and we can't keep going like that. We cannot wait for something to happen, we need to push it."
Munster (v Ulster) -- D Hurley; D Howlett, C Laulala, J Downey, L O'Dea; I Keatley, D Williams; D Kilcoyne, D Varley, BJ Botha; Donncha O'Callaghan, B Holland; Dave O'Callaghan, S Dougall, J Coughlan. Reps: M Sherry, M Horan, S Archer, D Foley, T O'Donnell, C Murray, R O'Gara, K Earls.