Exeter director of rugby Rob Baxter says clubs need clarity over whether the next rounds of European matches will be able to go ahead.
Exeter are due to travel to Montpellier on 23 January in the Champions Cup.
"We would like to see it try and go ahead as close to the format as possible," Baxter said.
Exeter host Glasgow Warriors next week before their final Champions Cup pool match in France seven days later.
Next week there are eight matches between British and French clubs, on both sides of the Channel.
"We're just preparing for our home game against Glasgow, which we've got to make an assumption will go unaffected," added Baxter.
"For us it's the following week when we need to know what our scenario is, so we can finalise our travel plans, but for other clubs it's a little bit more urgent than that, it's only a week away for them."
Exeter, who won the 2020 Champions Cup, beat Montpellier at Sandy Park last month before losing away at Glasgow a week later, and are third in their pool of 12 teams.
"I'd like to think the majority of clubs want the competition to try and be fulfilled this year rather than scratch it," added Baxter.
"But whether the weight of opinion is what I think, or whether the weight of opinion is that season's becoming a bit difficult or impossible to fulfil, I don't know.
"Those decisions will probably become a little bit more clear by the end of this week, when everyone's a little bit more aware of the French government position in relation to games of rugby."