The first would see a private equity backer buy Yahoo's US business, leaving the Daily Mail with its news and media operations, the newspaper said citing sources.
The second would involve a buyout firm taking over the entirety of Yahoo before merging the news and media departments with the Mail's online arms, including DailyMail.com and Elite Daily. The Mail would control that business and get a larger stake.
The possible deal would pit the Mail against other rumoured bidders, such as AOL owner Verizon and Tinder owner IAC.
It would also put the Daily Mail on stronger footing in the US where it has been gaining ground with its mix of news and celebrity updates. It came thirty-eighth in a top 50 ranking of US digital media sites with 66.7 million visitors in February, according to comScore.
Yahoo, which has been struggling to win online advertisers in the face of competition from the likes of Google and Facebook, has launched an auction of its core internet business.
It reportedly gave potential suitors an extra week to submit preliminary bids for the division, encompassing search, mail and news sites, as well as other assets.
Interest parties have until April 18 to make their case.