Discussions over the international tournament will be held next week after the French government recommended rugby clubs postpone upcoming European Cup matches with British teams.
The decision casts a doubt over the final two rounds of pool matches in the club competition, all scheduled to start next weekend.
The meeting, initiated by the French sport ministry, will look at the annual international tournament which is set to start on 7 February (AEDT) featuring France, England, Ireland, Scotland, Wales and Italy.
"This new variant of SARS-CoV-2 has increased transmissibility compared to those currently circulating in France, which then increases the risk of contamination," a statement from French authorities read.
"It's why all travel or holiday to Britain is strongly ill-advised.
"The French government is leaning, on a short-term basis, towards the adoption of measures that restrict or even bar French clubs from participating in games against team from the United Kingdom," it added.
Last week, European Professional Club Rugby (EPCR) and domestic competition organisers agreed to evolve protocol in the continental tournaments, which Top 14 outfits believed were too light.
Six fixtures in the European Champions and European Challenge Cups from earlier in the season have already been cancelled because of coronavirus cases affecting some squads.
After playing games against English sides in December, Bayonne and Pau recorded cases of the new variant among their staff.
The Basque side had threatened to pull out of the second-tier European Challenge Cup because of the infections.
The president of joint-record four-time European Cup winner Toulouse, Didier Lacroix, played down the current problems and said he hoped the tournament would be finished later in the year.
"There's enough time to make up for this competition," he said.
"I think it's a competition that's far from being distorted right now, it will take place more with a knockout stage, with things a bit harder," he added.