The new section will focus entirely on the Football League, with a match report on every professional game from the Championship down.
The paper is looking for £250,000 for the title package, which would include front-page branding, interior copy and a marketing campaign, with additional editorial support in sister title the Daily Sport.
Unlike the main paper, the pull-out will contain no advertising, chat lines or nakedness.
Paul Carter, editor of Sunday Sport, said: "This is an exciting new development in the Sunday Sport's history and offers the right brand a fantastic opportunity for exposure to a strong male audience.
"We already have strong interest from companies in the food and building sectors and will shortly review all the offers before making a final decision."
The launch of the new pull-out will be supported by an advertising campaign across TV, men's lifestyle magazines and online.
According to last month's Audit Bureau of Circulation figures, the national Sunday newspaper market has been suffering a steady year-on-year decline in sales.
In March the Sunday Sport's six-month average circulation was down 28.05% year on year to 101,894 copies.