Trinity Mirror's bankers NM Rothschild, which is running the auction, has shortlisted bids by Exponent Private Equity and Veronis Suhler Stevenson for the horseracing and betting newspaper.
The bank ruled out a bid led by Andy Stewart, chief executive of stockbroker Cenkos, and assisted by Kelvin MacKenzie, the former editor of The Sun, according to a report in The Times.
The duo were rumoured to have made an offer of a little over £190m, indicating that the remaining bids are likely to be in excess of £200m.
A key factor to the sale is the remaining contract between Trinity Mirror and Shekih Mohammed bin Rashid al-Maktoum, the title's owner and joint-ruler of Dubai. He has licensed the Racing Post name to Trinity Mirror in perpetuity and therefore must approve the potential purchaser.
The auction is likely to take another four to six weeks to conclude. The paper was put up for sale in December along with 138 Trinity Mirror regional newspaper titles.
Earlier this month Trinity Mirror reported a 13.8% fall in annual pre-tax profits to £185.4m, together with falling revenues blamed on poor "cyclical" advertising market conditions.
Despite this, Sly Bailey, chief executive director, received a pay package of £1.46m last year, up almost 50% from her remuneration received in 2005, according to the company's annual report.