The West Lothian club, which is working under a signing embargo due allegations of undeclared bonus payments, was served with a notice of complaint on Friday over claims Rankine also has interests in both Dumbarton and East Fife.
Privately, Rankine denies having any official involvement in the Fife side but has acknowledged that he is owed money by Dumbarton. It is thought that Rankine agreed to a five-year repayment plan when he sold Dumbarton for £1.6m in 2008 and that around £200,000 of that amount is outstanding.
Rankine, who owns 50% in Livingston's parent company Livingston 5 Ltd, has been in contact with Dumnbarton to try and strike a deal which will allow the Livingston stakeholder to sever all ties with their Championship counterparts.
However, should that debt remain unsettled then it is believed Rankine is willing to distance himself from Livingston, which could result in his stake being passed to other directors.
The signing embargo has resulted from claims that the club's former chief executive Ged Nixon paid undeclared bonuses of £30,500.