Around 2,000 people are employed by the airline which operates three routes from Leeds Bradford Airport to Belfast City, Southampton and Newquay.
The Exeter-based carrier was bought by a consortium consisting of Virgin Atlantic, Stobart Group and Cyrus Capital in February 2019 following poor financial results.
The consortium, known as Connect Airways, paid just £2.2 million for Flybe's assets but pledged to pump tens of millions of pounds into the loss-making airline to turn it around.
The holding of rescue talks with the Government indicates the financing requirements have become greater than expected.
Flybe has been hit by a series of problems, including falling demand, rising fuel costs and the weakening of the pound.
If it collapses, it would be the second UK airline to fail in four months, following the demise of Thomas Cook.
MPs on the BEIS select committee were scathing of the department for its handling of Thomas Cook's demise.
Business Secretary Andrea Leadsom was particularly criticised for not playing a more active role in discussions between bosses and the Government - with the negotiations and discussions taking place at the DfT.
Brian Strutton, general secretary of pilots' union Balpa, said he was "appalled" that the future of another airline "is being discussed in secret with no input from employees or their representatives".
He urged the parties involved to "stop hiding and talk to us".
Flybe is Europe's largest regional carrier, flying around eight million passengers a year to 170 destinations across the continent.
Connect Airways chief executive Mark Anderson said in October that the airline would be renamed Virgin Connect and he wanted it to become "Europe's most loved and successful regional airline".
Flights operated as normal on Monday morning.
A Flybe spokeswoman said: "Flybe continues to focus on providing great service and connectivity for our customers, to ensure that they can continue to travel as planned.
"We don't comment on rumour or speculation."
Spokesmen for BEIS and the DfT issued identical statements which read: "We do not comment on speculation or the financial affairs of private companies."
The airline began as Jersey European Airways in 1979, operating regional flights from Jersey.
Its route network grew and it was rebranded British European in 2000, before becoming Flybe in 2002.