Gus Poyet is looking to bolster his defence following the recent absences of veteran duo Wes Brown and John O’Shea through suspension and injury respectively.
Vergini is 25 and won the Argentine title with Newell’s Old Boys only last season, before joining Estudiantes.
Estudiantes president Enrique Lombardi said, as quoted by Sky Sports: "He wants to leave Estudiantes, and as he isn't a player that is considered as principle in the squad, we have accepted his departure.
"He wants to change team, and as there is a good offer that we have analysed, he will leave our club."
Uruguayan manager Poyet is also keen on Argentina goalkeeper Mariano Andujar and striker Ignacio Scocco as he looks to South America for reinforcements, according to the Mirror.
The Sunderland manager, 46, has vented his frustration with how difficult it is to sign British players, according to Football 365.
The former Chelsea and Tottenham player said: "So far players who've been in England, or British-based players, even if they are foreign, it is difficult to get them.
"Sometimes there are English players and they're on the bench at teams, not playing, and they should be playing in another team, but because we cannot pay them [enough], there's no chance of them coming.
"It's not because there's too many foreigners in England, it is because there are not enough British players playing at the top teams. It's the system that's wrong.
"There are teams who want too much money, there are teams who have no limit on what they pay. There are clubs with more money and big squads and it's impossible to get those players.
"I wanted to play when I was a player, but it's down to the player's character, the future they have and what they want."
However, he is still looking to tie up a deal for Brighton’s Scotland midfielder Liam Bridcutt, who, according to the Mirror, handed in a transfer request this week.
Poyet has bid £2.5m but his old club are reluctant to sanction the deal.
The Daily Mail are reporting that Ki Sung-Yueng will remain at the Stadium of Light despite his impressive form while on loan.
Swansea City manager Michael Laudrup could recall the South Korean midfielder to bolster his depleted midfield options but Poyet will be able to call on his services for the rest of the campaign.
Laudrup said: “I don't think bringing him back would help either of us. If I bring him back he will sit on the bench and maybe play some games.
'Imagine then, if Sunderland go to the Capital One Cup final, how that would affect the player mentally.'
Finally, Cabral completed his loan deal to Genoa, according to the BBC.
The midfielder hadn’t featured since August despite only signing from Basle in the summer and Poyet was keen to offload him.
He will remain in Italy until the end of the season.
image: © Daniel Coomber