PrintWeek has received calls from two employees claiming that the company has been placed into administration.
According to the High Court, a notice of intention to appoint an administrator was filed by MPC directors as far back as 13 April.
However, a spokeswoman at the court told PrintWeek that no progress had been made since. She added: "The only way to know more is to speak to the directors."
There is currently no dialling tone when calling the company's phone.
Unite has also alleged that employees have not been paid for almost two months and has issued a grievance against the company.
MPC founder Maurice Payne passed away in January. His sons Tom Payne and Finnbar Payne were appointed as directors of the company.
Also a director is John Davies, who was appointed on 18 April. Davies was formerly a director at Surrey printer DC Print, which went into liquidation in February.