The London-listed makeup and haircare company's shares closed 13% lower at 325 pence.
Revolution Beauty, whose products retail online and via high street stores including Boots and Superdrug, kicked off a sale process in May, and in June said it had received proposals from a number of parties.
True was the only company to submit a bid for the firm, which counts British online fashion retailer Debenhams (DEBS.L) as its largest shareholder, the people said, asking not to be identified because the talks were private.
However, the offer was seen as undervaluing the company, according to one source.
In a regulatory filing later on Thursday, Revolution Beauty said that its sales process continued to progress with ongoing engagement with a number of parties and that it was continuing to engage shareholders, including with respect to a potential equity raise.
True Potential declined to comment. Debenhams did not respond to requests for comment.
Mike Ashley’s Frasers Group (FRAS.L) had also explored buying the firm but said last month it had pulled out of the process.
Revolution Beauty, founded in Kent in 2014, floated in a post-pandemic listing boom at a valuation of nearly 500 million pounds, but its value subsequently cratered to around 12 million pounds, according to LSEG data.
It told shareholders earlier this year that it was reviewing its funding structure and considering raising funds from key shareholders after its annual sales slumped by more than a quarter.
The company is now likely to revive this plan if no other bidders materialise, the people said.
Debenhams' participation in any equity raise may hinge on the completion of its own debt refinancing plans, the second person said.
In May, Revolution Beauty also said it had begun talks with lenders over amending and extending the terms of its revolving credit facilities.
($1 = 0.7507 pounds)
