Eddie Howe's side have made a number of additions during the summer transfer window, sealing the signatures of Matt Targett, Nick Pope and Sven Botman among others.
However, the Magpies are now chasing two Leicester City stars, just one week away from the start of the new Premier League season.
Newcastle have already seen their £40million bid for James Maddison rejected, thought the club could yet make a second offer for the 25-year-old.
Leicester boss Brendan Rodgers was asked about the future of his attacking midfielder, with the manager telling BBC Radio Leicester: "He's still very much a player here.
"You see his performance, you see how happy he is and he's not a player we want to sell.
"It's not for me to put valuations on the players, it's not my side, but that might just cover three-quarters of his left leg, that price. He's a top player."
Rodgers was speaking after Leicester's 1-0 pre-season victory over Sevilla which saw both Maddison and Barnes start.
According to the Daily Mail, the Magpies have lodged an enquiry about 24-year-old Barnes.
The England international has made 147 appearances for the Foxes since making his first-team debut in 2016.
Maddison, on the other hand, has played 171 games for Leicester since arriving at the King Power Stadium from Norwich in 2018.