Sky News has reported that Kildare Partners, a London-based real estate investment firm set up by Ellis Short five years ago, is on a shortlist of bidders for the commercial premises.
These sit underneath railway arches across Britain and are used for a variety of businesses including bars, restaurants, bakers and mechanics. The railway stations above the network of arches are not included in the sale.
Other bidders are said to include CK Asset Holdings, the Hong Kong-listed infrastructure investor founded by the recently retired Li Ka-shing, Asia's richest man; a joint offer from funds managed by Goldman Sachs and Wellcome Trust, Britain's biggest medical research charity; Terra Firma Capital Partners, the buyout firm run by Guy Hands, the prominent financier; and a consortium comprising Blackstone, the world's biggest real estate investor, and Telereal Trillium, the property group owned by the Pears family.
Sky News is reporting people close to the process as saying bidders were looking at formal bids in the autumn likely to be worth between £1.3billion and £1.4billion.
The Government is selling off about 5,500 premises with the aim of raising funds for rail infrastructure investment.
Mr Short, a former president of the private equity firm Lone Star Funds, ended his nine-year stint as the owner of Sunderland earlier this year as the club suffered a second consecutive relegation.
His Kildare outfit invests only in Europe and has an affiliate called Curzon Advisers which manages its portfolio of assets.
The investment firm is of only a few British-based bidders for the Network Rail premises. And Sky News has reported its sources as saying bidders with a track record in the UK are likely to be treated more favourably during the later stages of the auction.
Goldman and Wellcome have invested together on previous occasions, including when they merged their student accommodation companies into a single enterprise, Vero Group, in 2016.
The auction is being run by Rothschild, and has already seen a number of other high-profile bidders eliminated - including a joint bid from Lend Lease, the property giant, and Legal & General, according to Sky's insiders.
Sky reports Network Rail's Commercial Estates arm has generated huge interest among private investors because of the hundreds of millions of pounds in rent it generates each year.
However, concerns have been expressed by some small business owners which lease sites from Network Rail - with new owners expected to hike currently low rents.
An action group called Guardians of the Arches is said to have been established to fight the planned sale.