World soccer's governing body FIFA has relaxed its normal rules about player-release for internationals because of the pandemic and worries about the impact of long-distance travel to areas with high case-rates. Clubs are expected to keep their players at home.
All 10 South American countries feature on the UK government's "red list" travel ban, which does not include exemptions for athletes and sports people. Any UK-based players who played in the games would face 10 days in hotel quarantine on return.
That in itself makes it difficult for clubs to consider agreeing to CONMEBOL's requests.
"I think everybody agrees -- we can't let the players go and play for their country and then quarantine for 10 days in a hotel. That's not how we can do it," said Liverpool manager Juergen Klopp, whose team includes Brazilian trio Alisson Becker, Fabinho and Roberto Firmino.
South American confederation CONMEBOL, which organises the qualifiers in the region for the 2022 World Cup, wants clubs to release their players for the March 25 and 30 games, but it is running out of options.
CONMEBOL's council will meet on Friday to discuss the situation and is in contact with FIFA as it searches for a solution.
But CONMEBOL is reluctant to play the games without European-based players and has not considered moving the fixtures to "bubbles" in Europe. It faces a scheduling problem, however as their continental championship, Copa America, is set for June in Argentina and Colombia.
With 14 rounds of matches still to be completed in the World Cup qualifying process, which is due to end in March 2022, there is limited space for the games.
"It is difficult to postpone the FIFA dates, there is no space, you cannot tighten the qualifiers," Ecuador FA president Francisco Egas told his local station Radio La Red.
"There is strong pressure from European clubs not to give up their players for the qualifiers. FIFA must be in the middle to help get an understanding," he added.
However, FIFA has limited influence. Quarantine rules are set by national governments.
Manchester United manager Ole Gunnar Solskjaer has struck a similar tone to Klopp.
"We've not sat down and made a proper call on that one, but it doesn't make sense if you lose your player for 10 days of isolation, of course it doesn't," Solskjaer said on Wednesday.
Solskjaer's squad includes Brazilians Fred and Alex Telles along with Uruguayan forward Edinson Cavani.
"We're the ones paying the players, and from what I understand FIFA have given the rules that they don't have to be released. So I would think that's going to be a hard call to make to let them go and play in red-list countries, yeah."
One option could be to play the games just before the June 11 start to the Copa America. One source indicated CONMEBOL may ask FIFA to create a special extra "window" for rearranged games.
FIFA and CONMEBOL did not immediately respond to requests for comment.