The Black Cats are keen to explore the South American market and want to use the cash brought in from selling Ross Stewart to pick up potential stars.
Uruguayan goal-getter Rodriguez, who plays for Liverpool of Montevideo, is firmly on their radar and played against Cerro Largo and Plaza Colonia over the last ten days, scoring once.
Black Cats talent spotter Harvey was in South America last week and he is chasing the 19-year-old.
Rodriguez is prepared to make the switch to Europe and Sunderland want to make sure they are in a position where they can move quickly for his signature.
Liverpool currently lead the Uruguayan Clausura and beat heavyweights Penarol earlier this month.
Rodriguez has found the back of the net three times in ten Clausura games and will be key if Liverpool are to remain in top spot.
All eyes will be on whether Sunderland prepare a bid to pounce on the striker when the January transfer window swings open for business.
