The bid is expected to come in ahead of the Monday deadline and will value the business at around $3bn (£2bn), some $2bn under expectations.
The lower-than-expected bid sent Yahoo's share price down by around 0.5 per cent in New York.
Previously bids for the internet company's core business came in between $4bn and $8bn, but reports in the Wall Street Journal earlier today suggest Yahoo’s evaluation is less than previously thought.
This second round is not thought to be the final round of bidding however, with at least one more on the cards and the offer could change by the final round.
It has been speculated that the bid value reported by the Wall Street Journal could have been intentionally leaked to the newspaper in order to drive down competing bids.
Yahoo’s core business, which makes up only a fraction of its $35bn market capitalisation, is suffering from declining revenues, down by 18 per cent in the first quarter to $859.4m.
Yahoo's market value is almost entirely tied up in its stakes in Chinese online retail behemoth Alibaba and Yahoo Japan.
It wouldn't be the first in this kind of acquisition for Verizon, which acquired AOL last year for $4.4bn.
Other potential suitors for parts of Yahoo are thought to be private-equity firms TPG, Advent International and Vista Equity Partners, along with a group led by Dan Gilbert, the founder of Quicken Loans.
The Daily Mail General Trust shocked the market when it expressed interest in acquiring the outfit.
Meanwhile The Children's Investment Fund (TCI) is building up a stake in Yahoo, it was yesterday reported by Sky News.
TCI, which was founded in 2004 by one of Britain's wealthiest men Sir Chris Hohn, has amassed a shareholding in Yahoo valued at hundreds of millions of dollars.
It was reported that TCI executives discussed the fund's Yahoo shareholding at an annual investor meeting held in London earlier today.