The Bundesliga club had an initial offer of €15m for the Japan international rejected by Nijmegen in mid-June.
According to De Telegraaf, Hoffenheim have since returned with a "serious offer" for the 22-year-old, with the move now said to be imminent.
Nijmegen had previously placed a price tag of €20m on their player. The report does not disclose the exact value of Hoffenheim's improved offer, but it appears to have satisfied the Dutch club.
In pursuing the two-time international, Hoffenheim have won out over VfB Stuttgart, who had also shown strong interest in Sano.
Hoffenheim finished fifth in the Bundesliga last season.
The central midfielder contributed nine goals and 12 assists in the Eredivisie last term. His performances helped NEC to a surprise third-place finish in the Dutch top flight.
Sano would become Hoffenheim's sixth new arrival of the transfer window, following the signings of Mats Rots, Patrick Wimmer, Cajetan Lenz, Alessandro Vogt and Sean Dulic.
The club's outlay before the Sano deal stands at close to €35m. Those fees are expected to be offset by the sale of Bazoumana Touré, who is on the verge of a €50m move to Newcastle United.
Sano is the brother of Mainz forward Kaishu Sano.