Virgin Atlantic is battling rival British Airways for ownership of Lufthansa-owned BMI.
Although International Airlines Group (IAG), parent company of BA and Iberia, reached a deal to buy BMI last month, Sir Richard Branson's Virgin Atlantic has remained in the race by signing a "terms of agreement" contract with Lufthansa.
Virgin will now be able to start due diligence and analyse BMI's books to find out what the acquisition would involve.
In the battle over BMI's coveted take-off and landing slots at Heathrow, Virgin is hoping to stop BA's owner gaining more dominance and having an even greater presence on the runways of the busy hub.
If the BA deal goes ahead it would mean that IAG owns more than half of Heathrow's landing slots, a move that angers Virgin and other rivals.
Although reports say the offer made by Virgin of around £50 million is half that of the IAG offer, Sir Richard's airline is hoping that the regulatory scrutiny that would accompany a BA-BMI merger will make it more attractive to Lufthansa.
Virgin's bankers are understood to be arguing that Lufthansa would be better off doing a cheaper deal with Virgin as it would be much quicker than a sale to IAG which would involve competition regulators.
If IAG is successful in its bid, the acquisition of BMI would significantly strengthen its position at Heathrow, giving it an additional 8 per cent of Heathrow slots, bringing its total to more than 50 per cent and therefore inviting scrutiny from regulators.
Virgin and IAG's interest in BMI show that the two airlines are undeterred by BMI's losses as it struggles to cope with the economic downturn and as people opt for lower-cost airlines such as easyJet and Ryanair.
Lufthansa took control of the British airline when its chairman, Sir Michael Bishop, sold his shares for £220 million two years ago.
The airline lost £140 million in the first nine months of this year and its total losses this year are likely to far exceed last year's £123 million, despite the airline downsizing by about a third.
A deal would help Virgin build a European feeder network for its long-haul operations based at Heathrow.
If the deal goes ahead, Virgin would be able to co-ordinate its schedules with BMI so that passengers flying from regional cities could transfer to long-haul Virgin flights in Heathrow, potentially increasing footfall on flights significantly.
Lufthansa declined to comment further on the future of BMI.