The 17-year-old Mastantuono made his debut for River in January 2024 and is widely regarded by the local media as the latest prodigy to emerge from Argentine football.
A talented left-footed finisher, he established himself as a starter under coach Marcelo Gallardo and soon became a key part of the Buenos Aires-based team.
"The sale is settled, in the final talks it remains to agree on some details," a club source told Reuters, who gave no further information about the transfer.
Mastantuono had been linked to other big European clubs such as Manchester United and PSG after attracting attention with a stunning free kick in River Plate's Superclasico win over Boca Juniors in April.
River intend to keep the attacking midfielder on loan at the club until December to complete their Copa Libertadores campaign, according to local press reports.
Argentina manager Lionel Scaloni recently called up Mastantuono for the first time for matches against Chile and Colombia in the South American qualifiers.
He could become the youngest player to make his senior debut for Argentina.