Saint-Maximin, signed from Nice last year for £16.5million, is under contract at St James’s Park until 2025.
However, the 23-year-old has been seeking improved terms at the Premier League club.
And the Daily Mail report that Saint-Maximin is to sign a new six-year deal at Newcastle.
Saint-Maximin was outstanding in the 3-1 Premier League win over Burnley at St James’s Park before the international break.