The Northern Echo reports that Manuel Pellegrini views Shelvey as a potential long-term partner for Declan Rice in the middle of the park at the London Stadium.
It has been a frustrating campaign for Shelvey. The 27-year-old has started just eight Premier League games this term, while he has only been brought off the bench on five occasions.
The Northern Echo reports that Benitez staying at St James' Park is likely to pave the way for a move to take place, and West Ham are confident that they will be able to complete a deal.
The report suggests that Benitez has his doubts about Shelvey's work-rate and is not sure that the former Liverpool man is buying into the team ethic.
With Benitez's concerns and Pellegrini's interest, it appears that a move could really suit all parties this summer. Newcastle's transfer kitty should receive a significant boost, while the Hammers would be landing a player who has a lot of quality if the best can be brought out of him.
Of course, once Shelvey is up and running for the Hammers, one manager will inevitably appear to have got the better end of the deal if a move takes place. But it appears that both Benitez and Pellegrini will be very satisfied if something can be agreed in the summer.