Sir Charles and TalkTalk's other main shareholders have offered to inject £150 million into the company to avert a potential debt crisis, the paper reported.
The company's lenders are pressing Sir Charles and TalkTalk's other main shareholders, led by private equity house Toscafund, to provide cash to unlock a rescue deal.
The banks providing TalkTalk's £330 million revolving credit facility are understood to be looking to reduce their exposure to as little as £150 million when it is up for refinancing in November.
That would require Sir Charles and his fellow shareholders to provide £180 million in new equity. Negotiations between the two sides are ongoing.
Sir Charles and Toscafund delisted the business from the stock exchange three years ago by loading it with more borrowing, much of which is now due.
The company faces two large repayments totalling more than £1 billion in the coming months: the £330 million revolving credit facility later this year and £685 million of bonds in February next year.
TalkTalk is currently seeking to raise £450 million from the sale of a large stake in its wholesale arm to Macquarie. The proceeds have been earmarked to help pay off some of the company's debt.
Attempts to sell the wholesale arm are part of a broader break-up plan. In September, a syndicate of the group's shareholders bought its business unit for £95 million, and its consumer arm is also expected to be put up for sale.
TalkTalk declined to comment.