The 54-year-old McClaren has been in charge at St James' Park for nine months but they have been anchored in the relegation zone for much of the season while a January spending splurge failed to spark a revival.
With only 10 matches remaining to secure their Premier League survival, Newcastle are second from bottom having lost three successive games and five of the last six.
McClaren left the training ground at 1400 GMT, according to local media, with a fog of uncertainty surrounding his position.
Sky Sports television reported the club were in "advanced talks" with Spaniard Benitez about succeeding the former England boss on a three-year deal.
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Benitez, who has also had spells at Chelsea, Valencia and Napoli, was sacked by Real Madrid in January.
(Reporting by Toby Davis; Editing by Tony Jimenez)
