Press Association Sport understands the Black Cats have made an enquiry over the 25-year-old, who has 24 senior caps for his country.
Should they manage to strike a deal, Banega would become the third Argentinian to head for Wearside this month, with goalkeeper Oscar Ustari and central defender Santiago Vergini due to make their debut in Saturday's FA Cup fourth-round tie against Kidderminster.
Poyet had earlier signed Spanish full-back Marcos Alonso on loan from Fiorentina.
The Uruguayan has voiced his intention to bring in up to four more players after Alonso's arrival, with Brighton midfield Liam Bridcutt one of his main targets for this month's transfer window.
But Sunderland have wasted little time in implementing the head coach's plans in the wake of the departure of director of football Roberto de Fanti last week.
The Black Cats certainly look a more attractive proposition now than they did at the start of the transfer window, having reached the final of the Capital One Cup in midweek.