The two firms were reported on Friday to be in exclusive talks over a possible deal.
US internet firm Yahoo announced in February that it was looking at “strategic alternatives” for its core internet business.
Verizon declined to comment on the reports.
A formal announcement is expected on Monday, which is later today before US markets open for trading.
Over the last few years Yahoo has struggled to keep up with the changing internet advertising landscape, with some analysts arguing that it has failed to remain relevant in many of its core markets.
Chief executive Marissa Mayer, who took the helm in 2012, has made little progress in returning the company to profit.
Last week the firm reported a $440m loss in the second quarter, but said the board had made “great progress on strategic alternatives”.
The reported price tag for the deal is well below the firm’s $125bn market value at the height of the dot.com boom.
But BGC analyst Colin Gillis wrote recently: “We expect any offer in the range of $5-plus billion should be accepted by the Yahoo board to bring the process to a close.”
The US telecoms giant is expected to merge Yahoo with AOL, to create a digital group capable of taking on the likes of Google and Facebook.
Verizon bought AOL – another faded internet star -in a $4.4bn deal last year, which gave it ownership of the Huffington Post, Techcrunch, Engadget and other news sites.
Shortly afterwards, Verizon announced it would start combining data about its mobile network subscribers – which is tied to their handsets – with the tracking information already gathered by AOL’s sites.
By doing so it said it could deliver more “personalised” ads.
A host of other firms were reported to be interested in buying Yahoo’s core internet assets including AT&T and the owner of the Daily Mail.
In April, the firm shortlisted about 10 potential buyers, but fortunately, Verizon has gone closer than any other firm.