Mr Johnson has offered £10m in a three-year loan to owners Patisserie Holdings plc, which the company said would provide "immediate liquidity".
"Without an immediate injection of capital, the directors are of the view that that is no scope for the business to continue trading in its current form", it stated.
Patisserie Valerie owner Patisserie Holdings CAKEP.L said on Friday that Chris Marsh, its suspended finance director, was arrested by the police on Thursday night and had been released on bail.
The company, with professional advisers from accountants PwC, spent 24 hours investigating the financial status of the company.
Hertfordshire Police told the BBC: "A 44-year old man from St Albans has been arrested on suspicion of fraud by false representation".
"He has been released under investigation".
"The board has now reached the conclusion that there is a material shortfall between the reported financial status and the current financial status of the business".
The company's future was thrown into question earlier this week after it uncovered fraudulent activity around its financial accounts.
Patisserie Holdings said it would update the market in due course.
It said that while the findings were preliminary and subject to change it now believed the group had net debt of approximately £9.8m.
Landlords for at least two Patisserie Valerie locations in London - in Hammersmith and Edgeware Road - cancelled their lease agreements with the company over breach of contract.
The company has been struggling to stay afloat after "significant, and potentially fraudulent, accounting irregularities" were reported on Wednesday.
Mr Marsh was later suspended from his role and accountancy giant PwC drafted in to look through the company's books.
The firm also revealed this week that HMRC had filed a winding up petition against its main trading subsidiary, Stonebeach, over an unpaid £1.14 million tax bill.
Patisserie Holdings - which owns additional brands such as Druckers, Philpotts and Baker & Spice - trades from more than 200 stores and also has a partnership with Sainsbury's, with branded counters present in the supermarket.
Chairman Luke Johnson is said to be considering stepping in with funds that could help save the business.
Mr Johnson, a serial entrepreneur, is the largest shareholder in Patisserie Holdings, and had a 37% stake in the business ahead of the rescue deal.