Virgin Atlantic said talks were “ongoing and constructive”, but added that it is also looking at raising cash from the private sector.
Many airlines have been struggling as revenues have dropped amid travel bans.
However, sources at the airline told the BBC that the firm had not set an end of May deadline for finding a buyer.
They added: “Because of significant costs to our business caused by unprecedented market conditions which the Covid-19 crisis has brought with it, we are exploring all available options to obtain additional external funding.”
In the blog post, he said: “We will do everything we can to keep the airline going – but we will need government support to achieve that”.
He added that his luxury island resort Necker Island could be used as collateral to help secure state aid for Virgin Atlantic.
The Department for Transport said: “The aviation sector is important to the UK economy, and firms can draw upon the unprecedented package of measures announced by the chancellor, including schemes to raise capital, flexibilities with tax bills, and financial support for employees.”
A spokesperson added that they were willing to consider individual firms’ situations, after all alternatives had been explored, “including raising capital from existing investors”.