River have yet to respond to the offer for 27-year-old Quintero, but will consider it seriously.
If they do sell him, $7m (€5.95m) will go straight into their coffers after taxes and similar fees.
Quintero joined River from FC Porto in 2018 on an initial loan deal before the Argentine club made it permanent.
After recovering from an ACL injury, Quintero has not started regularly for River, which has put his future in doubt.
Quintero wants to play at next year’s World Cup in Qatar after representing Colombia in the 2014 and 2018 editions.
However, that could work against Shenzhen with the Chinese league having less exposure than others.
Clubs from the USA, UAE and Qatar have shown interest in Quintero, who must now consider whether he wants to play in China.