Desmond has stated that he will not bid for Hollinger's other assets, despite the tax implications involved in splitting up the group, which also owns the Chicago-Sun-Times, The Spectator and the Jerusalem Post.
Last month Desmond sold off his pornography titles, including Asian Babes, to improve his chances of winning the race for The Telegraph.
The second round of bids, to take place next week, is being seen as little more than a repeat of the first round of bids in order to attract new offers. According to reports Desmond is becoming increasingly exasperated by the drawn-out process.
Insiders claim that Desmond's rival Daily Mail & General Trust, owner of the Daily Mail, is unlikely to increase its bid and is understood to be working in partnership with others, such as venture capitalist Cinven, to submit a bid for the entire group.
Other bidders include investment firms Candover and Collins Stewart and the US publishing giant Gannett, which owns USA Today.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the .