Billionaire Mr Day, who is behind The Edinburgh Woollen Mill Group, earlier in April acquired more than half of the company’s shares through holding company Spectre, triggering a mandatory takeover bid.
But the retailer told shareholders on Friday to “take no action”, deriding the offer as too low and adding that it is to embark on a cost-cutting exercise.
Bonmarche said that, in light of the fourth quarter, it is planning a number of “cost reduction actions across the group and anticipates starting the implementation of these shortly”.
Rejecting Mr Day’s overtures, the firm stated: “In view of Spectre’s position as the majority shareholder in Bonmarche, the board has sought to engage with Philip Day to discuss the future plans for the business for the benefits of all stakeholders.
“The board will be writing to shareholders with its formal response to the mandatory cash offer once the offer document has been posted by Spectre.
“In the meantime, Bonmarche shareholders are strongly advised to take no action in relation to their Bonmarche shares.”
Earlier this month, Mr Day bought more than 26 million shares, representing 52.4% of the struggling firm.
At just 11.445p per share, the offer represents a significant discount and values the whole entity at just £5.7 million.
Spectre said at the time that it would undertake a profitability assessment on Bonmarche’s estate of more than 300 stores and shutter under-performing sites or reduce costs by cutting the number of staff or seeking a lower rent.
It comes after Bonmarche issued its third profit warning in just six months in March.
The womenswear retailer said it has seen “significantly weaker” trading since the start of the month, reversing a bounce-back in January and February after it resorted to heavy discounting to shift stock.
Mr Day’s name has been linked with several retail turnarounds. At the weekend he was named as a bidder in the race for collapsed womenswear brand LK Bennett, though he later withdrew from the process.
Last year he was one of the potential buyers circling House of Fraser, which was eventually sold to Sports Direct owner Mike Ashley.
His other investments include Peacocks, Proquip, Austin Reed, Country Casuals, Jaeger and Jacques Vert.