Investment company Festina Lente Partners, led by Peter Crowley and Neil Hughes, is offering between £180- and £190-million for the newspaper, which saw off a new rival called The Sportsman in 2006.
Former Racing Post editor Alan Byrne is advising the Irish consortium, which consists mainly of property developers and is not connected to Coolmore.
The Racing Post was founded in 1986 by Sheikh Mohammed and he still holds rights to the title after selling the paper for £1 in 1998 to Trinity Mirror who then published the rival Sporting Life newspaper.
Trinity Mirror, which closed down its own paper and has since then published the Racing Post, owns three national newspapers headed by the Daily Mirror and regional titles.
It took the decision to sell the Racing Post at the end of last year following a strategy review and had reportedly put a price of £200 million on the specialist publication.
FL Partners, negotiating final details with Trinity Mirror over the proposed sale, appears to have gained the upper hand from other bidders, including one advised by Brough Scott, the current editorial director of the Racing Post.