Longstaff is a free agent at the moment, with the original deal at Newcastle having run out at the end of the past season.
The Times have claimed that the 20-year-old has been persuaded to stay at St. James Park and will commit his long-term future to the Magpies.
Leeds United - who will play in the Premier League next season after winning automatic promotion from the Championship - want to sign the England Under-20 international midfielder, and so do Italian club Udinese, according to the report.
However, Longstaff has reportedly decided that he will stay at Newcastle, with the club having managed to persuade him to put pen to paper on a new deal.
The young midfielder made six start and three substitute appearances in the Premier League for Newcastle this past season, scoring two goals in the process.
Longstaff also made three starts and two substitute appearances in the FA Cup for Steve Bruce’s side during the 2019-20 campaign.