Manager Rafa Benitez is also understood to be a fan of Ndiaye, and had the Senegalese midfielder scouted earlier in the season, while he was still a Galatasaray player.
The Magpies wanted to bring the 27-year-old to Tyneside in January, but lost out to Stoke for the player's signature.
Following Stoke's relegation from the Premier League, Ndiaye is expected to be on the move again, with Newcastle a possible destination.
According to the Chronicle, Newcastle want to bring the midfielder in should new Stoke boss Gary Rowett accept a cut-price deal for the player.
Newcastle are believed to be willing to offer as much as £20m, as well as potentially including forward Dwight Gayle in the deal as way of a further incentive.
Rowett is known to hold a significant interest in Gayle, who has a prolific goalscoring record in the Championship. As such, a deal that saw the forward go one way and Ndiaye the other could be very interesting to both parties.
Ndiaye made 13 Premier League appearances for Stoke, scoring twice, after his January move to England. He had made 17 league appearances for Galatasaray earlier in the season.
In Turkey, Ndiaye earned a reputation as a powerful and dynamic midfielder capable of playing in the box to box role or in a more advanced position.
He even earned himself a reputation as a reliable goalscorer during his time with Osmanlispor - where he moved to Galatasaray from.
Ndiaye has 17 senior international caps for Senegal and is with the team at this summer's World Cup.