The Magpies are hopeful of agreeing a deal for the Italian international.
The 23-year-old, who has played 130 times for the Milan club, has been labelled 'the new Andrea Pirlo'.
He made 48 appearances for the club in all competitions last season as they finished fourth in Serie A and reached the Champions League semi-finals.
Tonali began his career at Brescia in 2020 before making his move to AC Milan permanent a year later.
He helped them win the Serie A title in the 2021/22 season.
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Tonali already has 14 appearances for the Italy senior side, but will also captain the Under-21s at this summer's European Championship.
It would be another statement of intent from Eddie Howe and Newcastle to land the highly-rated midfielder, who has previously been linked to Arsenal and Chelsea.
Howe wants to push Brazil international Bruno Guimaraes further up the pitch next season, as they look to build on their brilliant 2022/23 campaign.
The Magpies are believed to be keen on signing two new midfielders this summer.
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Howe is also keen on long-term target James Maddison, who was relegated with Leicester, but face competition from Tottenham.
Inter Milan's Nicolo Barella has also been mooted as a potential target.