Jacob Murphy scored 10 goals for Norwich last season and was one of the outstanding performers for England at the U21 European Championship in Poland.
Newcastle will hand in an improved offer, with Rafael Benitez keen to strengthen his squad for the new Premier League season.
The English Premier League club have made just two major signings this summer, with winger Cristian Atsu coming in from Chelsea and Florian Dejeune arriving from Eibar.
Murphy has spent time on loan at Swindon, Southend, Colchester and Coventry, as the U21 English international has a contract at Norwich until the summer of 2021.