Douglas and Howell have been talking to potential investors about backing the launch of a Sunday tabloid to compete with Rupert Murdoch's Sun on Sunday.
It is thought that they have struggled to secure enough investment to launch the tabloid, so have approached Desmond about the purchase of the Daily Star Sunday, which is a loss-making paper.
Advisers acting on behalf of Douglas and Howell met Martin Ellice, MD of Northern & Shell, just weeks ago.
It is understood a meeting between the advisers and Desmond is scheduled to take place in the coming weeks.
Douglas admitted to Media Week that she was talking to Desmond about the possible sale, but said other options were on the table.
One well-placed source claimed Desmond and Douglas are at the contractual stage of negotiations. But a source close to Northern & Shell denied a sale was likely, saying Desmond continually talks to different parties about his portfolios.
Should Douglas succeed with the bid the Daily Star Sunday would be rebranded as The News on Sunday, the title Douglas is on record as saying she wants the tabloid to be called.
Last month, Trinity Mirror rebuffed a tentative approach for its Sunday tabloid, The People. Douglas said that a possible deal for The People could still prove an option.