Manager Oliver Glasner says it would be "irresponsible" for Crystal Palace to play two games in three days following a fixture pile-up after reaching the EFL Cup quarter-finals.
The Eagles are due to host Manchester City on Sunday, 14 December, KuPS in the Conference League on Thursday, 18 December, and visit Leeds United on Sunday, 21 December.
Arsenal, their last-eight opponents in the EFL Cup, want their tie played on Tuesday, 16 December. If Palace are told to play on that date, it will mean three games in five days, four in eight, or five in 11.
"I can't believe this won't be fixed," said Eagles boss Glasner. "It would be irresponsible for the players and we have a responsibility for them and we have to look after their welfare, but not just ours at the club.
"I was really upset when I heard it for the first time yesterday. I couldn't even believe that they were considering this."
Uefa's European calendar now stretches across 10 midweeks, rather than the six as it did two seasons ago, with the Champions League, Europa League and Conference League each given a standalone week for exposure.
It has caused a huge logistical headache, with the third round of the EFL Cup having to be seeded and played across two weeks to keep clubs in the Champions League and Europa League apart.
That was a pretty straightforward fix, but with the Conference League held on consecutive weeks in December, and the final round of games muscling into the regular slot for the EFL Cup quarter-finals, it was a matter of when, not if, a Premier League club had to play two competitions at the same time.
There was a narrow escape last season, with Chelsea losing at Newcastle United in the fourth round. This time, the EFL has an issue.
