The Chinese club had an initial bid of €8.5m turned down by River. Of this, River would have received just under €6m.
According to TyC Sports, Shenzhen’s new offer would see River pocket €9m in total, an offer they are likely to accept.
Quintero, 27, is an idol at River after scoring against hated rivals Boca Juniors in the 2018 Copa Libertadores final.
The talented Colombian arrived at River from FC Porto at the beginning of 2018 and has won four trophies at the club.
But it seems that his next destination could be the wealthy Chinese Super League with Shenzhen FC.