Cake Box said it rejected an approach from an Australian fund manager River Capital.
In a stock exchange release, the AIM-listed baker said River Capital offered 160p per share in June.
The share price peaked at 142.5p at the end of the month, while it started the month at 125p per share.
“The board unequivocally rejected the indicative approach as materially undervaluing the company and no further discussions with River Capital have taken place,” the company said.
Cake Box floated in London in 2018 at a price of 108p per share, with the stock currently trading at 159p.
Last month, it said full-year adjusted underlying earnings (EBITDA) had fallen by nearly a quarter, although inflation was starting to soften "which will support margin progression over the medium term".