The 25-year-old Portugal international has been a target for the likes of Arsenal, West Ham and Spurs in recent seasons, but the report claims Alan Pardew will launch a move this summer as the club looks to replace Demba Ba.
The Senegalese striker departed for Chelsea in the January transfer window, and having secured their top flight status for another season, the Magpies want a big-money striker to fire them up the table next term.
The price tag could be an issue though, with Sporting Braga eager to hold out for £16m.
The report claims Newcastle want an agreement whereby £8m is paid up front, with add-ons taking the figure closer to Braga's asking price.
Spurs and Arsenal have both been linked with the Portugal striker in the past two seasons, but Eder's value has skyrocketed following impressive performances in the Champions League.
Spurs are in the market for a new forward this summer, after injuries and Emmanuel Adebayor's poor form in front of goal hampered their push for Champions League qualification.
But Newcastle are likely to rival the north London clubs for many of their targets, including Eder.
The report claims St Etienne hotshot Pierre-Emerick Aubameyang, Vitesse's Wilfried Bony and Ajax's Siem de Jong have all been watched by the north east club.