Sky News has learnt that Portman Dental Care, the company set up by Mr Waley-Cohen in 2009, is in talks with a number of trade and private equity bidders about a takeover which could value it at more than £300m.
The part-time jump jockey, whose Cheltenham victory came on Long Run, remains a big shareholder in Portman, having sold a stake in it to Livingbridge, a buyout firm, in 2014.
The business now trades from roughly 60 practices across the UK and is understood to have grown its profits substantially since its last accounts were filed at Companies House for the year to September 2016.
Mr Waley-Cohen was due to ride Walk In The Mill in Saturday’s Grand National but the horse was declared a non-runner after it was found to be lame.
The proposed sale of Portman follows Bupa’s takeover of the much larger chain Oasis in an £835m deal in February last year.
A string of takeovers led by private equity firms such as Nordic Capital in the European dental market have led to the creation of a cluster of large-scale operators in the sector.
Another big player in the UK market is MyDentist, which is backed by the private equity group Carlyle and has about 450 practices.
The price paid by Bupa for Oasis surprised analysts, who had pencilled in a much lower valuation for the business.
Sources said that it had fuelled hopes at Portman that it could also attract a premium price.
The auction of Portman, which did not respond to requests for comment, is being run by Moelis, the investment bank.
Livingbridge said in a statement issued to Sky News: “We do not comment on market rumour and speculation.
“Portman Dental Care is the fastest-growing privately led dental group in the UK and is well placed to build on the strong momentum it has generated in recent years.”