Sky News has learnt that Neighborly, a US-based provider of home services owned by the giant private equity firm KKR, is among a number of parties which have expressed an interest in buying Pimlico Plumbers.
A private equity investor who had expressed an interest earlier in the sale process said on Wednesday that a sale of Pimlico Plumbers could be imminent, although they cautioned that it was unclear whether Neighborly or another suitor would be the eventual buyer.
Reports earlier this year suggested that Mr Mullins was likely to fetch a price in the region of £100m after hiring advisers from Cavendish Corporate Finance to identify new investors.
The tycoon, a vocal opponent of Brexit who has become an outspoken figure on a range of economic matters, founded Pimlico Plumbers in 1979 with a single second hand van.
He has grown it into one of the capital's most ubiquitous businesses, with its prominent branding displayed on a fleet of vehicles driven by its roughly-400 staff.
The company is now run by Scott, Mr Mullins' son.
Neighborly would be a logical buyer for Pimlico Plumbers as it seeks to extend its international reach.
It was bought by KKR from Harvest Partners, another investment firm, just two months ago.
Neighborly owns a range of franchise-based home services brands, including HouseMaster and Mr Appliance.
Pimlico Plumbers and KKR declined to comment, while a spokeswoman for Neighborly did not respond to a series of requests seeking comment.