Unless Air France can put together a rival bid quickly, then the administrators are expected to hand control of Air Liberte to BA this week.
A Virgin spokesman confirmed the approach, but indicated that the deal Virgin Express struck with Sabena on Friday to operate a scheduled service between Heathrow and Brussels was occupying management's attention.
"We have been approached by a number of parties but our main priority is working with Sabena," he said.
Virgin beat off competition from Ryanair to secure the Sabena deal and will operate its first flights today, using two new Boeing 737 aircraft to provide the service.
It regards a London link to the Virgin Express network as more important than the acquisition of another domestic airline.
However, if Air France succeeds in finding other partners for its consortium then a rival bid would represent a blow for BA.
BA's chances of winning control of Air Liberte soared last week when its main rival, Nouvelles Frontieres, withdrew. Groupe Rivaud, the banking group which had been in the Nouvelles consortium, then threw its support behind BA.
Acquisition of Air Liberte is important for BA if it is to consolidate its position in the French domestic market where it is represented by TAT, which has the weakest position.
The deal would more than double BA's market share to over 20 per cent. That is still well below the 60 per cent commanded by Air France-controlled carriers, but would provide a credible foundation on which to develop the business.
Industry sources say if BA does not secure control of Air Liberte, it will withdraw from the French domestic market.
Robert Ayling, BA's chief executive, said last week that he expected both Air Liberte and TAT to break even within three years.
Under the terms of its proposals to acquire Air Liberte, the BA consortium will inject pounds 78m into the ailing airline. BA will take a controlling 70 per cent stake.
The introduction of Groupe Rivaud as a French partner will help deflect criticism that Air Liberte was passing into foreign ownership. BA has stressed that under its proposals most of the jobs and routes would be preserved and that Air Liberte would remain a French airline.
However, if Air France does intervene it will play the nationalist card without hesitation and will attempt to stir up a whispering campaign against BA.
Competition between the two carriers in France is already intense ahead of the liberalisation of the European air market next year.
Analysts suspect that Air France would like to mount a spoiling bid but that the price it would have to pay and the time in which has to do so makes the task difficult, particularly if Virgin, which has been studying Air Liberte for the past two months, does not participate.
Virgin Express will have its hands full digesting the Sabena deal since it is taking over operational control more swiftly than it had anticipated. It will be flying to Brussels today without even advertising the inaugural single fare of pounds 29.Reuse content