The Black Cats have reached an agreement with Estudiantes for the 25-year-old centre-half, but have yet to get the deal over the line.
Poyet is, however, of the opinion that a switch is close to completion and is delighted to see Vergini doing all he can to ensure that his next challenges lies in England.
He told the Sunderland Echo: "If it goes through, we have to give plenty of credit to the player because he wants this badly. That gives you a big hope as a manager.
"I think when you bring in too many from abroad and you are expecting all of them to adapt to the football and the country quickly, you are making a big mistake. It won't happen."
"We're getting closer. It's not been easy, we've been going forwards and backwards. One day it's looked 'yes' and the next it's looked 'no'.
"With such extremes, it's been difficult. But now I'm hopeful."
The Uruguayan coach is believed to be focusing plenty of attention on the South American market, but he admits to being wary of bringing in too many Premier League novices.
He added: "I think when you bring in too many from abroad and you are expecting all of them to adapt to the football and the country quickly, you are making a big mistake. It won't happen.
"We are looking everywhere. England is part of everywhere and I think the possibility of bringing in a player that is English or British and a foreigner, is exactly the same.
"We try to make sure that we bring in players that have already played in England first, if it is a foreigner.
"If not, we look at someone who has already been away from home and experienced different languages.
"That's not always possible, but we're doing well."