According to estimates in the industry, the American electronics giant submitted an acquisition offer of $400 million.
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However, only few investors have been exposed to the offer, and the companies are likely in the very first stage of the talks.
Sources in the industry believe Waze is worth at least $1 billion, and $400 million is not considered a series offer for investors.
It is unclear how Waze will merge into Apple and what will happen to Waze's development center in Israel if and when the acquisition is completed.
The two companies have yet to comment on the report.
Waze has raised a total of $67 million so far from a series of investors, including Israeli funds Vertex Venture Capital and Magma Venture Partners, American Kleiner Perkins and Li Ka-shing's Horizon Ventures.
This isn't the first acquisition offer Waze receives from a technology giant. According to past reports, Facebook expressed an interest in cooperating with the navigation application, and one of the suggested options was an acquisition.
Waze says it saw a jump in downloads of its app after Apple Chief Executive Tim Cook, in an unusual move after the launch of iPhone 5, suggested that customers download rival mapping services like Waze while Apple improves its own maps.
Nitzan Sadan and Reuters contributed to this report