Ashkenazi is a popular former Israeli military chief of staff who held the post during the three-week war in the Gaza Strip from December 2008 to January 2009.
He is widely viewed as a credible challenger to Netanyahu, either with the Labour-led Zionist Union coalition or the centrist Yesh Atid party, though he has not made his intentions clear.
Attorney General Yehuda Weinstein issued his decision to drop the investigation on Wednesday, citing a lack of evidence, Israeli media reported.
Its origin was a dispute between Ashkenazi and then defence minister Ehud Barak that became known as the Harpaz affair.
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A document emerged in 2010, determined to be fake, purporting to lay out plans by Barak's allies to smear Ashkenazi.
The fake document was alleged to have been put together by an ally of the former chief of staff, who has always maintained his innocence.
The two men were at odds at the time in part over who would succeed Ashkenazi as military chief of staff.
Netanyahu has been prime minister for a total of nearly a decade.
Last week he was declared the winner of a one-candidate race to lead his Likud party in what was seen as a move to outmanoeuvre rivals although the next general election is not due until 2019 at the latest.