The ferry group has almost 4000 employees and operates more than 30,000 sailings a year on major routes including between the United Kingdom, France and Ireland.
Dubai ports firm DP World bought the company in 2019.
P&O said it had halted all sailings but was not going into administration and would make an announcement later on Thursday.
It did not reply to a request for comment on the Times report and it was not immediately clear how many workers would be affected.
Transport minister Grant Shapps said in parliament his officials would urgently seek conversations with the firm, particularly over concerns about its workforce.
P&O has a fleet of more than 20 ships that sail across the English Channel, North Sea and Irish Sea.
Like all travel companies, it will have been hit by two years of COVID-19 restrictions which disrupted tourist travel.
The transport workers' trade union RMT said it was disturbed at the reports and had advised its members to remain on board ships.
"We have instructed our members to remain onboard and are demanding our members across P&O's UK operations are protected and that the Secretary of State intervenes to save UK seafarers from the dole queue," RMT General Secretary Mick Lynch said.
P&O tweeted to its customers that services would not be running "for the next few hours".
"P&O Ferries is not going into liquidation," a company spokesperson said in a statement.
"We have asked all ships to come alongside, in preparation for a company announcement. Until then, services from P&O will not be running and we are advising travellers of alternative arrangements."
Last year DP World reported an 11 per cent jump in 2020 revenue and said it would continue to invest in the segment even as it acknowledged that P&O Ferries and Ferrymasters had been through a "particularly challenging time" due to COVID-19.
The BBC reported that a P&O message sent to staff said the company announcement "will secure the long-term viability of P&O Ferries".
