According to Daily Mail, Mike Ashley is prepared to sanction a £36million move for the 22-year-old.
The report adds that the Magpies want to get the deal done this week and they have been keen on the player since January.
Hoffenheim were thought to be pushing for a fee of around £40m but Newcastle want to finalise the deal for £36m.
Joelinton has done well in Germany and he should prove to be a good addition to the Newcastle side. He scored 11 goals in all competitions last season.
The Magpies have lost Salomon Rondon and Ayoze Perez this summer and they are in desperate need of attacking reinforcements.