Citing a person familiar with the matter, the newspaper said Verizon was expected to meet the Monday deadline for the second round of bidding.
A third round of bidding was expected, the report said.
Verizon, which owns AOL, has emerged as a leading contender to take over Yahoo as other big names are reportedly dropping out, according to US financial media.
Britain's Daily Mail eyeing Yahoo bid: US media
Yahoo, the Internet pioneer that has fallen behind rivals such as Google and Facebook, has said it is studying the possibility of a sale as it pursues efforts to revive growth, focusing on mobile users.
Yahoo chief executive Marissa Mayer has so far failed to revive the company, which in February announced it was cutting 15 per cent of its workforce and narrowing its focus as it explored "strategic alternatives".
A media report last month said billionaire Warren Buffett had agreed to work with Quicken Loans founder and chairman Dan Gilbert on a bid for the Yahoo core assets.
Gilbert is also the owner of the NBA's Cleveland Cavaliers team.
Private-equity firm TPG was also expected to make a second-round bid, the Wall Street Journal said, citing a person familiar with the matter.
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