The owner of Moonpig, the online greeting cards retailer, is among a pack of prospective suitors eyeing bids for Notonthehighstreet.
Sky News understands that Exponent, the private equity firm, has held preliminary talks with advisers to the online portal for selling personalised gifts such as books, jewellery and toys.
It was unclear on Wednesday whether Exponent, which is in the process of preparing a stock market listing for Moonpig, had submitted a firm offer for the company.
It emerged last month that Notonthehighstreet, which was founded in 2006, had hired the investment bank Evercore to conduct an auction that could see it valued at more than £200m.
Some private equity executives believe the business, which is based in Richmond and employs more than 150 people, is likely to attract offers of around £150m.
A number of trade bidders and private equity groups are thought to have expressed an interest in buying the company, which acts as a marketplace for 5,000 small business-owners.
Set up by Holly Tucker and Sophie Cornish, Notonthehighstreet has become a popular destination for consumers wanting to buy personalised gifts.
Its prominent customers include the Duke and Duchess of Cambridge, who used the site to buy Prince George a personalised dressing gown that was seen when they met the then US President Barack Obama in 2016.
In its latest annual report for the 2019 financial year, the company said it had served more than 2.5 million customers during the period, but seen total revenues flat compared to the year before at just over £35m.
Notonthehighstreet is not unusual among online retailers in being loss-making, although it trimmed its after-tax loss in the year to March 2019 to £1.5m.
It said it had done so after focusing its marketing activity on its most profitable customers.
The company's backers include Hubert Burda Media, the German publisher, which became a shareholder in 2016 as part of a £21m fundraising.
Other investors include Index Ventures and an arm of the asset management giant Fidelity.
Notonthehighstreet is chaired by Darren Shapland, the former finance chief of J Sainsbury.
Mr Shapland's appointment in 2015 sparked speculation that Notonthehighstreet was preparing to float on the stock market, but its performance since then, and its shareholders' preference for a sale, have led it to launch the auction with Evercore.
Last year, the company appointed a former HelloFresh executive, Jill Davenport, as its chief executive.
Exponent declined to comment.
