News International is reported to be bidding for the paper along with private equity firms Exponent and Montagu.
According to a report in The Times, Exponent is in talks with the Racing Post's editorial director, Brough Scott, about joining its bid.
Other bidders include former investors in the failed The Sportsman newspaper, including Irish investor Dermot Desmond and Andy Stewart, chief executive of stockbroker Cenkos.
The sale, which is being run alongside the disposal of Trinity Mirror's Midlands and South East regional newspapers, including the Birmingham Mail, is expected to be concluded by May.
Yesterday, 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.
Revenues were down 4.8% or £51.5m to £1.03bn, with a steeper drop of 5.3% to £472.4m at its national newspaper division, which includes the Daily Mirror. At its regional division, revenues fell 8.1% to £468.4m.