According to Express, the Hammers submitted a £10m bid for the playmaker earlier but Newcastle have turned it down.
However, West Ham have no plans of backing down and they will return with an improved offer for Mike Ashley and co.
Shelvey has not played too often for Newcastle this season but he is still a key member of the squad. Losing him halfway through the season could be a major blow for Benitez.
His side is already struggling with the lack of creativity and Shelvey is the best passer in the side. Newcastle cannot afford to lose the former Liverpool man.
Meanwhile, the Newcastle midfielder could complete West Ham’s midfield and Pellegrini’s interest in him makes a lot of sense.
The £80,000 per week midfielder can run the play from deep and he would be the ideal partner for Declan Rice. Mark Noble is past his peak and Shelvey would be the ideal replacement. The arrival of Nasri has already improved the creativity in West Ham’s midfield and Shelvey could complete the puzzle for Pellegrini.
It will be interesting to see if Pellegrini can convince the Magpies to part with their star player in January. If West Ham manage to pull off the deal, it would be a solid addition to their side.