Sources told ESPN that the deal would be comprised of a two-year loan with River having the option of making the move permanent after a year or after the full term of the loan.
The move has been rumored for weeks with Olé reporting that each option would be for 50 percent of Barco's rights for a total of $8 million.
River recently agreed to transfer midfielder Julian Alvarez to Manchester City for around $27m, and with that influx of money comes more flexibility in the transfer market, including the pursuit of Barco.
The Argentine giants are also interesting in acquiring New York City FC striker Taty Castellanos, though with the MLS side asking for north of $15m, it still remains to be seen if a deal will get done.
Barco, 22, was signed by Atlanta in 2018 to great fanfare and a reported fee of $15m from Argentine side Independiente. But a combination of injury, inconsistent form and instability in the managerial ranks has seen him fall short of expectations.
Over four seasons Barco has made 107 league, cup and playoff appearances, scoring 19 goals. While he has appeared for Argentina's youth national teams, he has yet to make an appearance for the senior side.