Kilmarnock could be set to forfeit three matches following their coronavirus outbreak.
Killie's Scottish Premiership clash with Motherwell was postponed at the Ayrshire club's request on Friday after their entire first-team squad were instructed to self-isolate by health officials following six positive Covid-19 cases.
The Scottish Professional Football League launched an investigation and chief executive Neil Doncaster confirmed it could lead to Motherwell being awarded the points.
The league had little option but to postpone the game as available players need to submit a negative test two days before a fixture.
Doncaster told BBC Radio Scotland's Sportsound: "Clearly, it's very concerning that you have six positives within one club.
"That's something we need to investigate in conjunction with the health authorities, because the protocols in place are designed to ensure there shouldn't be transmission within a club.
"Where we've had positives elsewhere this season, on the whole the games have gone on universally. The exceptions were the Aberdeen and Celtic games but that ultimately was a government decision.
"If there are found to be concerns, that would go to a disciplinary in front of a sub-committee of the SPFL board, which has broadly unlimited powers to impose a sanction.
"We hope very much that all protocols have been followed. We'll keep an open mind."
Killie are due to face Falkirk and Dunfermline in the Betfred Cup in the course of the next 10 days, with a decision due on Monday on whether they will be able to play. The SPFL can award the points to Killie's opposition in that competition.