Both Lufthansa and BMI declined to comment on reports that the German carrier is planning to sell its minority take in the British airline.
Lufthansa holds a 30% minus one share stake in the carrier which is part of the loss making BMI group and has approached both BA and Virgin Atlantic to see if they wish to buy.
However the major BMI shareholder, Sir Michael Bishop, chairman of the group, who has a 50% plus one share controlling interest, is reportedly opposing Lufthansa's plans.
While Virgin's chairman Sir Richard Branson has repeatedly said he would like merge his airline with BMI, it is not thought likely he would want just a minority holding in the group.
BA also rejected the approach as it fears with some justification that such a purchase would run foul of the EC competition regulations.
Lufthansa bought the first part of its minority holding in its star Alliance partner in 2000 but BMI, like many other airlines post 9/11, has suffered big losses.
Now that it is on the route to recovery, thanks partly to the success of its low cost carrier bmibaby, it is not thought likely that Sir Michael would want to sell any of his stake.
One of BMI's assets which attracts Virgin is its possession of 13% of the slots at London Heathrow Airport all of which the airline uses for short haul routes.
Virgin which is keen to expand its long haul business out of the airport has fewer than 3% of its prized slots.
BA has 40% of the airport's slots and it is likely that an additional 13% would be regarded as giving it too dominant a position at one of the world's biggest airports.