The Magpies are continuing their search for attacking reinforcements after missing out on Hugo Ekitike during the transfer window, who eventually made the move to Paris Saint-Germain from Reims.
Having been put off by Leeds United's £35m valuation of Jack Harrison, Eddie Howe's side have also pursued moves for the likes of Anthony Gordon of Everton, and more recently, Kamaldeen Sulemana from Ligue 1 side Rennes.
However, Leicester's Barnes has become the latest target according to The Sun, but as a result, the Foxes have placed a huge £50m price tag on the 24-year-old's head, the report suggests.
Despite enduring an injury-hit campaign in a more difficult year for the one-cap England international last season, Barnes still managed to score 11 goals and register 13 assists in 47 appearances for Leicester across all competitions.
Barnes has also managed to net three times in four appearances during pre-season so far, as he, and Leicester, go in search of an improved 2022-23 campaign after missing out on European football following an eighth-placed Premier League finish last time around.