Haaretz newspaper said on its website that the two companies had agreed terms and were about to sign for a price "exceeding $1 billion".
Business daily Globes said the purchase price was $1.3 billion. Neither report identified its sources.
"We don't comment on rumour and speculation," a Google spokesman told AFP about the Israeli media reports.
There have been previous reports that first Apple and then Facebook wanted to acquire the Israeli start-up.
Globes said that those deals fell through partly because Waze insisted that its local staff be kept on.
It said that Google, which has bought two Israeli firms in the past, has a local office.
Haaretz said the agreement called for the US Internet search engine giant to pay the full amount in cash.
"In addition, Waze's research and development centre will remain in Israel for at least three years, as will the company's CEO, Noam Bardin. Waze will retain its independent identity both as a company and as a brand," it quoted "sources" as saying.
"Facebook had sought to fold the company into its California headquarters," Haaretz added.
Waze, which claims more than 40 million users, describes itself as an app bringing together "the world's largest community of drivers who work together to fight traffic, and save time and gas money on their daily commute".
Company officials could not immediately be reached for comment.
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