CNBC, citing unnamed sources close to the situation, said Yahoo's board of directors will meet Friday to review offers ahead of a final round of bidding expected to lead to a decision by mid-July.
California-based Yahoo declined to comment.
Yahoo shares were up slightly more than a percent to $37.42 as the close of trading neared on the Nasdaq exchange.
Yahoo, which has been eclipsed by rivals such as Google and Facebook, is studying the possibility of a sale as it pursues efforts to revive growth, focusing on mobile users.
Yahoo chief executive Marissa Mayer has failed to revive the company since taking the helm in 2012.
Mayer has been working to revive growth and made priorities of what she refers to as "Mavens" mobile, video, native advertising and social media.
In February, Yahoo announced it was cutting 15 percent of its workforce and narrowing its focus as it explored "strategic alternatives" that included selling itself after spinning off its multi-billion-dollar stake in Chinese Internet colossus Alibaba.
Yahoo's struggling Internet business took a hit in May with the loss of a long-time contract to manage the Internet portal and search for US telecommunication giant AT&T.
Yahoo reported a loss in the first quarter of this year as it courted potential buyers and examined other strategic options.
Yahoo averted a proxy battle for control of the company earlier this year with a compromise that added four new board members, including a hedge fund chief who has been critical of management.