The A Bola report claims Benfica president Luis Filipe Vieira rejected the offer outright, and didn't even consider it as it fell well short of the club's valuation.
The Argentine international has been linked with Manchester United since last summer.
And with Nemanja Vidic set to depart at the end of the season, many expect United boss David Moyes to move for another central defender at some point.
But while the Premier League's transfer window has shut, the Russian window remains open until the end of the month.
That means Zenit remain in negotiations with Benfica over a deal for Garay, and the report claims they had planned talks for after the Benfica versus Sporting Lisbon game last weekend.
That was postponed and has been rearranged, but A Bola notes that it may still be Garay's last game for the club.
As part of the €10m offer, Zenit were reportedly willing to include Portuguese international Luis Neto. The former-Siena defender joined Zenit last year.
United defender Rio Ferdinand could also call time on his career at the end of the season, which would leave Moyes with a massive hole to fill at the heart of the United defence.
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