The Scottish Premier League has launched an investigation into whether majority Hearts shareholder Vladimir Romanov has broken its rules.
Vladimir Romanov has claimed he was misquoted
Romanov has denied allegations he was quoted making against the Old Firm and Scotland's referees.
SPL secretary Ian Blair told BBC Sport on Monday: "We are not charging them with anything.
"But we are putting them on warning that we are examining any potential breach of the rules."
It is understood that the letter sent to Hearts identifies various allegations attributed to Romanov in a Russian magazine.
A wide range of sanctions, including fines, suspensions and deduction of points, is available to the SPL board if its rules have been breached.
"We have written to Hearts to ask for information to allow us to enquire whether there has been any breach of SPL rules," said Blair.
Hearts have 14 days to respond to the letter or the SPL board will go forward with the matter on the basis of available evidence at the moment.
A spokesman for Romanov, who is back in Lithuania on business, told BBC Scotland that the Hearts owner is trying to track down the reporter who wrote the original story to clarify exactly what he said.
Meanwhile, the independent tribunal looking into Hearts' appeal against the £10,000 penalty imposed by the Scottish FA on Hearts as a club has finished.
But an announcement will not be made until the parties involved are notified first of the decision.
That is likely to be within seven to 10 days.
The Tribunal comprised Lord Maclean, Gordon Law and Andrew Renwick.