Mr Ashley first bought into Mulberry in 2020 and has subsequently increased his stake to 37pc.
The Ong family’s vehicle said it “appreciates that Frasers is a supportive minority Mulberry shareholder” but that it would not sell and urged him not to proceed with an offer.
“Challice understands that in order for Frasers to deliver the possible offer, Frasers would need to become interested in more than 50pc of the issued Mulberry Shares,” it said.
“Challice notes that without its support, it is not possible for Frasers to achieve this; Challice hopes that by making its position clear, Frasers will be encouraged to announce that it does not intend to make an offer for Mulberry.”
Last week Frasers Group criticised what it said was a lack of a plan to improve Mulberry’s fortunes, predicting that the fashion house would need to raise more funds in the coming years “unless there [was] immediate and very real change at the company”.
It added: “Despite the [lack of plan], Mulberry’s catastrophic results, its necessity for emergency funding and difficult market backdrop, Frasers strongly believes it can provide the appropriate insulation and investment to support a much-loved British brand.”
Frasers Group declined to comment on Challice’s latest rejection.