The 21-year-old full-back looks set to become the seventh signing of the summer at the Stadium of Light as the Black Cats enter into personal negotiations with him.
The 21-year-old full back made his debut for the Buenos Aires-based club in 2011 and has been a permanent fixture in Ricardo Gareca's first team ever since.
But he could now be closing in on a move to the Stadium of Light, the Black Cats having entered "advanced negotiations" by the end of June, where Paolo Di Canio has already brought in six new faces so far this summer.
Velez chairman Miguel Callelo told Radio Rock & Pop: "[Velez and Sunderland] talked about the payment conditions and the values. We reached an agreement quickly. Now Gino Peruzzi's representatives and the English club need to reach an agreement.
"When this kind of proposal comes, it's hard to say no. If we turn them down, we might never receive this kind of proposal again."
Peruzzi has four senior caps for Argentina and started in its 1-1 draw in a World Cup qualifier against Ecuador in June.