Benitez almost became West Ham boss back in the summer of 2015, only for hometown club Real Madrid to swoop in for the experienced boss.
The 'Hammers' are on the lookout for a new manager after opting against retaining Moyes' services following the expiry of his six-month contract.
The likes of Manuel Pellegrini and Paulo Fonesca are also unerstood to be serious targets, but the aforementioned source claims that West Ham co-owner David Sullivan is hoping that his relationship with the Spaniard will be enough to lure him to London Stadium.
Benitez has just a year left to run on his deal on Tyneside and is looking for certain assurances to be made before commiting his future to the club.
In the meantime, there is understood to be a £6m release clause in his contract that West Ham are considering activating.