The Daily Mail says Benitez, 60, was approached by the Cherries this month after they sacked Jason Tindall.
The Spaniard - who remains one of the main favourites to be next permanent manager of Celtic - was available having just quit Super League side Dalian Pro to be with his England-based family.
Benitez is no stranger to a brutal Championship season, having guided Newcastle to the title in 2017.
The Cherries have since made interim boss Jonathan Woodgate their manager until the end of the season.
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