The ERC are in constant contact with both clubs - and all others as games in all participating countries come under threat from the bad weather - in a bid to make sure that the match takes place.
The top of the table clash could be moved to a Saturday afternoon start and Montpellier have been asked to take this into account in their travel arrangements.
Connacht, who have accumulated 17 points from four straight wins so far, are also looking at alternative venues and supporters will be informed of any changes on the Connacht Rugby website, www.connachtrugby.ie.
Meanwhile, the all-weather training facility developed at the Sportsground in recent months is proving invaluable during the big freeze.
Connacht's recent Magners League games at home to Leinster and the Dragons have fallen by the wayside because of the frost and snow.
But the all-weather training facility developed behind the Connacht Branch headquarters at the Sportsground has ensured that Michael Bradley's squad can continue to train and prepare for their upcoming matches.
The facility, located close to the new gym, was completed a few months ago and with pitches throughout the country under a blanket of frost and snow, it is proving invaluable.
Bradley said: "It's great because it allows us maintain some level of normality during a difficult time for all squads.
"Like other sides, we have had to adapt our training programme but the all-weather facility, along with the gym here at the Sportsground, is great because it allows us get on with things as best as we can."