As for its own 65 per cent stake, Virgin said it "remains committed to the long-term growth of the Velocity business and expects to remain the majority investor".

However, there is speculation Virgin could reduce some of its holding through an IPO to raise funds to improve its precarious financial position.

Velocity has about 9 million members and made $110 million in earnings last year.

Virgin sold the 35 per cent shares of Velocity to Affinity in 2014 for $336 million. The whole business is now valued between $1.5 billion to $2 billion.

A change of ownership at Velocity will be another significant move under Virgin's new chief executive, Paul Scurrah, who took control of the airline in March and is trying to improve its financial returns after it ran at a loss for the past six years.