Benitez, who has also been linked with a move to Newcastle United, is said to be the Hammers' no.2 choice behind David Moyes to replace Sam Allardyce, whose contract expires at the end of the current campaign.
Along remarkably same lines, the Daily Mirror are also reporting Benitez is West Ham's second choice to succeed Allardyce.
Meanwhile, sports betting website Oddschecker details the latest odds on the Benitez - West Ham speculation and the reports have caused a clear movement.
Indeed, the Newcastle-linked coach is now fourth favourite overall, outright favourite with one bookmaker at a price of as low as 2/1, while he is ranked at 6/1 and 4/1 by others to move to West Ham.
The Spaniard would certainly prove an interesting addition at Upton Park and would be a much bigger departure from Allardyce, which is not what could be said for the similarly defensive Moyes.
As for the previous rumours linking Benitez to Newcastle, that talk seems to have cooled of late but the 54-year-old is stillfifth favourite with bookmakers to succeed John Carver at St James' Park.