Scottish FA chief executive Ian Maxwell has written to all 10 Championship clubs asking if they want to continue playing or suspend their league.
Maxwell has asked for replies no later than close of business on Monday.
In an email sent on Friday evening, he mentions that one Championship club has already publicly called for a suspension of all football.
Maxwell did not name the club in question but it is understood to be Inverness Caledonian Thistle.
Earlier this week their manager John Robertson told the media he was “worried about 26 players” under his charge, along with their families.
The comments were discussed by the joint response group, leading to the email from the SFA chief executive.
All Scottish football below the top two tiers has been suspended for a minimum of three weeks because of a surge in Covid-19 cases.
Championship clubs have been allowed to continue their truncated 27-game season, which began in mid-October, on the condition that they test players and staff weekly for Covid-19.
Maxwell wrote: “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.”
BBC Scotland has contacted the Scottish FA for comment.