The former AC Milan and Manchester City star is a free agent after leaving Genoa over the summer.
Now 33, Balotelli is eager to play on and TMW says contact is being established between the veteran and River Plate.
River coach Marcelo Gallardo is driving the move, convinced Balotelli can make a big splash in Argentina next year.
Gallardo hopes for talks directly with Balotelli to sound him out about the prospect of moving to South America for a late career swansong.