The Sunday People has been suffering from long-term declining sales but still posts operating profits of £6m.
With a price tag of close to £50m, possible bidders are expected to include David Sullivan, publisher of the Sunday Sport, and Richard Desmond, the proprietor of the Daily and Sunday Express and the Daily Star, the Express Group's strongest performer.
Sullivan is already understood to have tabled an unsuccessful bid for the Sunday People in the last 18 months.
For Trinity Mirror, the problem has always been that the Sunday People competes head to head with sister paper the Sunday Mirror in a market dominated by the News of the World. Trinity Mirror recently tried to reposition the People as a more downmarket title while moving the Sunday Mirror upmarket.
However, the Sunday Mirror's attempt was thwarted by the strength of the Mail on Sunday.
Shares in Trinity Mirror had risen 5.5p at 12.50pm today to 462p.