In a letter to staff on Friday, the firm wrote that employees would be "laid off with immediate effect".
The Glasgow-based bakery, which employs around 250 people, said that "no final decision" had been taken on redundancies but all jobs were at risk.
Companies House states on its website that there is an "active proposal to strike off" the firm.
Morton's Rolls accounts for the year to 31 March 2022 were required to be filed by 31 December and are now overdue.
Last month, compulsory strike-off action was suspended on 9 February, two days after it was announced by Companies House.
But in the letter to staff on Friday, the firm wrote: "The company is ceasing to trade with immediate effect.
"The directors have taken steps to ensure that the business can continue in some form.
"But it is likely that this will be with a reduced workforce across the business."
Bill Kidd, SNP MSP for Glasgow Anniesland, told BBC Scotland he was "taken aback" by the letter and had arranged a meeting with the company's management.
He said: "There has been issues in the past but we've got good relations with Morton's Rolls, they are terrific company and are a very important employer in Drumchapel.
"Morton's Rolls is a famous name and we want to ensure that is maintained and even developed into the future
"Everything that can be done to save this business will be done."
Morton's Rolls was originally founded by Bob Morton and Jim Clarke in 1965 at their bakery near Drumchapel, in the west of Glasgow.
Over the years, Morton's expanded its product range to include cakes and savouries.
The company's flagship product is its traditional crispy roll.
For the year to the end of March 2021, the company reported a loss of £262,00 on turnover of more than £11.8m.
Morton's Rolls has been approached for comment.