Earlier this week Napoli president Aurelio De Laurentiis said the Spaniard could stay at his club "for the next five years" if he wanted to.
But ESPN's sources say Benitez will quit the Sao Paulo when his contract expires in June, putting the Hammers on red alert as they prepare to make a decision on the future of Sam Allardyce in May.
The 54-year-old led Napoli to the Coppa Italia and third place in the Italian top flight in his first season in charge but has been criticised this campaign for failing to mount a serious bid for the Serie A title.
He did help them win more silverware, though, in the form of the Supercoppa and they are in the semi-finals of the Europa League.
The sources claim Benitez is ready to 'seek a new challenge' and would favour a return to these shores where he won the Champions League and FA Cup at Anfield and the Europa League in West London.
The former Valencia boss' career has been laden with trophies but the feeling among some Hammers fans is that, like Alan Curbishley before him, the Spaniard once described as the 'luckiest manager ever' by Sir Alex Ferguson is simply too dour and does not play attacking football home and away true to West Ham's roots.
But Benitez has also managed and won trophies with Inter Milan and his statistics speak for themselves. From an almost identical number of games as the man he could replace, Benitez has a remarkable 464 wins from 912 games with a ratio of 50.88%. Perhaps the more striking statistic, though, is that his sides have amassed a positive goal difference of 579.