Sky News understands that the current owner of Great Rail Journeys (GRJ) has kicked off a period of exclusive negotiations with Duke Street Capital about a deal expected to be worth around £100m.
GRJ provides escorted rail tours in dozens of countries, including on the world's most famous train, the Venice Simplon-Orient-Express.
The company was established as Mac's Tours by Ian Macbeth and Howard Trinder, who as workers at the state-owned British Rail were entitled to big discounts on foreign rail journeys.
It took in outside investment for the first time in 2005 when it struck a deal with Primary Capital, before selling again in 2013 to ECI Partners.
The talks with Duke Street come nine months after Duff & Phelps, the advisory firm, was hired to help ECI find a buyer for its stake.
Duke Street is one of the UK's best-known private equity investors, having backed companies including The Original Factory Shop, Payzone and Voyage Care, a care provider for people with learning disabilities.
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The firm, which has generated favourable returns for investors over the last decade, recently invested in Arosa Cruises, which focuses on holidays along some of Europe's longest rivers.
Duke Street could not be reached for comment on Tuesday.