An email sent out to the 10 teams stated that one unnamed club wanted all football to be stopped as Scotland endures its second lockdown since the start of the global pandemic.
The Championship was allowed to continue on the condition that every team tests staff and players after all football below the second tier was suspended.
BBC Scotland quotes Maxwell’s email as saying: "One SPFL championship club has publicly taken the position that all football should be suspended.
"The Scottish FA would like to understand the position of your club... please confirm if you are content to continue under the current exemption or whether your club considers that the Championship should be suspended."
Hearts currently lead the Championship by five points after 10 games played of their truncated 27-game season.