Sky News reports the carrier has broached the subject with shareholders and other financial stakeholders as the typically quieter winter months loom.
Citing "City" sources, while a final target figure is yet to be agreed, any such move by the end of the year would require a cash injection from founder Sir Richard Branson.
Virgin Atlantic declined to comment, Sky said.
Sky additionally reports any plans Virgin Atlantic had for an IPO, initial public offering on the stock market, have been parked. It was reported in August Virgin was considering such a move.
Branson’s Virgin Group remains the airline’s majority shareholder with a 51% stake; Delta Air Lines holds the other 49%.
Virgin Atlantic hasn’t sold shares publicly in its 37-year history, and doing so would likely involve Branson giving up overall control.
Branson, though, last week sold $300 million (£223 million) stock in space tourism operation Virgin Galactic.
Last September, Virgin Atlantic secured £1.2 billion in what was the largest of several efforts to secure the cash the carrier needed to survive the Covid crisis.
However, although flights on Virgin’s most lucrative routes between the UK and US have resumed, there remains significant pressures on airline balance sheets.