The announcement follows weeks of speculation over the future of Mulberry, with Mr Ashley initially lodging a £83m offer late last month.
Frasers said at the time that it was making an offer to avoid “another Debenhams situation”, fuelled by concerns over the luxury company’s finances.
Frasers later increased its offer to £111m, although Mulberry rejected both after branding a deal “untenable”. This was on the basis that its largest shareholder refused to sell.
Challice, which is controlled by Singapore-based billionaire hotelier Ong Beng Seng and his wife Christina, owns 56pc of Mulberry.
Frasers’ criticism comes after claims it was excluded from talks regarding a Mulberry fundraising last month.
The retailer later took part in the process but said it had “significant reservations” over whether it would be enough to prop up the business.
It also suggested that Mulberry would probably have to raise more cash in the near to mid-future.
The concern over the handbag maker’s finances came as Frasers launched a fresh call to Mulberry to give it a board seat to help steer the business.
Frasers said it had already made this request on several occasions.
The Telegraph revealed earlier last year that Mr Ashley’s lieutenants had met with Mulberry’s chairman and chief executive to request a voice in its boardroom.
At the time, Frasers was understood to be frustrated over the lack of transparency in Mulberry’s business in Asia.