Flybe is the biggest airline operating at Birmingham Airport, employing around 400 people at the airport where it currently runs around 750 flights a week on 29 routes.
But the Now regional airline put itself up for sale last week after warning over profits earlier in the year.
Virgin Atlantic, part owned by Sir Richard Branson, is thought to be vying with Stobart to buy Flybe and is interested in its take-off and landing slots at London's Heathrow Airport.
In a statement to the City, Virgin confirmed it was "reviewing its options in respect of Flybe which range from enhanced commercial arrangements to a possible offer for Flybe".
Flybe shares were up nearly 20 per cent in stock market trading during the morning, at 11.4p, as a result of speculation over a possible deal.
The Exeter-based carrier is battling challenging conditions in the airline industry and has been hit with falling demand and a £29 million hit from rising fuel costs and the weak pound.
Flybe has 78 planes operating from smaller airports including Birmingham, London City, Southampton and Norwich, and flies to destinations across the UK and Europe.
It carries around eight million passengers a year and Virgin would look to attract customers into its long-haul network via Flybe's domestic routes, according to reports.
Trade unions have already raised concerns over the impact of a Flybe's sale on the carrier's 2,300 employees.
In half-year results announced last week, Flybe saw cost-cutting help lift underlying pre-tax profits to £9.9 million from £9.2 million a year earlier.
But statutory pre-tax profits for the six months to September 30 more than halved to £7.4 million from £16.1 million a year earlier.
It saw group revenues fall 10 per cent or 2.4 per cent on an underlying basis to £409.2 million after it cut capacity by 9 per cent.