Newcastle have been chasing Joelinton since January but were unwilling to get drawn into further protracted negotiations as Hoffenheim initially demanded over £40m.
However, meetings got underway on Wednesday morning in the hope of reaching an agreement by Thursday for a fee in the region of £36m.
Joelinton scored seven league goals in 28 games last season.
Hoffenheim confirmed via their Twitter account: "He is in concrete negotiations with a Premier League club. It may be that he leaves us."