The Rugby Football Union has expressed "concerns" over whether the 2021 Women's Six Nations will be completed.
The men's tournament begins on 6 February but dates for the women's event, which is normally played on the same weekends, are yet to be announced.
The competition is a key part of teams' preparations for the World Cup, which starts in September.
A Six Nations spokesperson said organisers are "working on plans to try and hold the championship".
But RFU head of women's performance Nicky Ponsford told BBC Sport: "I do have concerns about how well we're going to be able to get through this period."
The latest coronavirus lockdowns across Europe have complicated planning, with England the only fully professional side in the tournament, while France are semi-professional.
The majority of players from Ireland, Wales, Scotland and Italy are amateur, creating issues around testing, bubbles and travel.
Ponsford added: "I'm relatively confident about how England are going to be able to deal with it, but there are different challenges in different unions."
In 2020, three Women's Six Nations fixtures were cancelled because of coronavirus.
England - who sealed back-to-back Grand Slams when they beat Italy in November - were the only home nation to play all their Women's Six Nations fixtures in 2020.
Scotland were only able to play three of their five matches, while Wales and Ireland played four.
This year Ireland, Scotland and Italy's Six Nations fixtures may also double as World Cup qualification matches given none of the three sides have yet sealed their place in rugby's showpiece.
Ponsford said there was "more planning to do over the next week to 10 days" to see "if we can get through the Six Nations or get through as much of it as we possibly can".
When asked if the tournament could move to a different window, Ponsford explained that before Christmas it had been decided "it was the right thing to do to leave it where it was".
However, she added "the world has now changed again".
"It's becoming more challenging," Ponsford continued. "There's a lot of things to put into the mix."