Murray suffered medial ligament damage to his right knee in the 36-8 success against the Catalans on December 8, with an initial prognosis suggesting a recovery period of six weeks. That length of absence was set to rule him out of the weekend's trip to Kingsholm and the final round home tie with Edinburgh a week on Sunday but head coach Rob Penney and Murray's housemate Mike Sherry are hopeful he will return earlier than anticipated.
"There always was a chance for Conor. Hopefully the work the medical team has been doing will come to fruition," said Penney, who has a major injury concern regarding Murray's understudy, Cathal Sheridan.
"The running and jumping and hopping over chairs and exercises are sure to have the desired result!" laughed Sherry. "Seriously, though, he has been very disciplined and we'll only have to wait and see if all the work has the desired outcome."
The chance to welcome Murray back into the fold for a crucial fortnight of action would be a huge boost for a Munster side who currently top Pool 6 by five points from Gloucester, with the English outfit a point clear of Perpignan and two ahead of Edinburgh.
Munster know that a bonus-point victory at Kingsholm would guarantee a place in the last eight of Europe's top tournament for the 15th time in the last 16 seasons.
The 2006 and 2008 Heineken Cup kings were comfortable winners over the Cherry and Whites when they first met in Limerick back in October but Sherry insists they won't be taking anything for granted, especially on the back of a first domestic defeat since mid September.
"Kingsholm is a great stadium, Gloucester have amazing support and a magnificent tradition and, because they absolutely have to win this game, they will be very dangerous opposition," Sherry, who is currently sidelined with a cruciate knee injury, told the Irish Independent.
"Munster are in a great place in the Rabo League and Heineken Cup. It's a very happy squad scoring plenty of tries and points.
"We don't like to lose any matches, especially interpros up in Belfast, but I suspect that result will only stir the lads up a bit more. There's been a tradition that we don't play that well on the week before the Heineken Cup but in fact I don't think we played poorly against Ulster."