Many national newspapers are now running the reports, with The Mirror among those backing up that he has been sounded out.
The Spaniard is available after his quick fire dismissal at the ruthlessly impatient Real Madrid, and if he is appointed then expect fireworks in the upcoming Tyne-Wear derby, and throughout the rest of the season as he battles fierce rival Sam Allardyce, the Sunderland manager.
There is no love lost between the pair, who have a feud stretching back almost a decade.
It began at Anfield when Benitez's Liverpool took on Allardyce's Blackburn, and after Fernando Torres scored a second goal, the Reds boss made a gesture with his hands as if to suggest the game was over, which Benitez denied.
Sir Alex Ferguson used the incident to attack Benitez at the time describing it as 'beyond the pale', reported The Guardian.
Allardyce himself was just as critical, commenting: "I think if everybody has a look back at his gestures you will see them as pretty dismissive to me and the Blackburn Rovers team as a whole.
"I was hugely disappointed by those gestures. I think they were disrespectful and quite humiliating. Having looked at them again this week, I think I'm right and everybody will see why I'm complaining."
In his autobiography serialised in The Sun last year, Allardyce said that he loves it when his teams beat Benitez's: "Benitez wouldn't talk to me at all and that just made it all the better when we won. I can't stand people who disrespect me the way he did."
Allardyce even claimed Benitez wrongly basked in Liverpool's 2005 Champions League success when he was manager, and the glory belonged to the players instead.
He said: "Of course he can say he won the Champions League with Liverpool, which is something I never did. But it was nowt to do with him. I don’t blame Benítez for claiming credit but as managers we know the truth. It’s like when you make a substitution in desperation and it comes off. You get all the credit for your tactical brilliance when it’s often just luck.”
Benitez did not take that lying down, reacting on Spanish, as quoted by the Daily Mail belittling Allardyce's achievements in the game.
He said: "Do you know who Sam Allardyce is? Do you know how many trophies he has won? Well that’s my answer.
"It is what happens when someone has a book to sell. His opinion does not have a lot of value."
Expect the rivalry to continue at full tilt if Benitez gets appointed, and for this reason alone it would be worth it for the neutral to see Newcastle fire McClaren and get the Spaniard on board.