Sky Sports are reporting that the winger is set to join the Championship club on loan until the end of the campaign.
Murphy, signed from Norwich City in the summer of 2017, has been on the fringes of Rafa Benitez's first team this season.
Benitez, however, said last week that it would be difficult to allow the 23-year-old – who started last weekend's FA Cup defeat to Watford – to leave unless players arrived in this month's transfer window.
Newcastle have today signed midfielder Miguel Almiron and left-back Antonio Barreca.
Benitez is keen to sign another winger before tonight's transfer deadline.
United's manager has identified Nantes' Anthony Limbombe as one potential target.