The Scotland international has not played since January 29's 1-0 win over Stoke City because of an Achilles injury and, despite having returned to training, was left out of Saturday's 4-1 Premier League defeat to Arsenal.
Poyet opted not to risk the 26-year-old for the trip to the Emirates Stadium but feels that the former Wolves man could play a part as Sunderland seek to seal their first major trophy since the FA Cup in 1973.
|9/2||Sunderland are 9/2 with Bet365 to win the Capital One Cup|
"He trained with us on Saturday and he's a possibility for the team at the weekend."
Though well beaten, the Wearsiders registered a consolation goal against Arsenal through substitute Emanuele Giaccherini. It was only the Italian's fourth of the campaign but, with goal difference a potential factor in Sunderland's fight against relegation, Poyet believes that the strike could yet be crucial in the end-of-season shake-up.
"It's been difficult for Giacchy," he added. "He's one of those players that you try to give minutes to when you can. For different reasons, I haven't been able to but he's always been knocking on the door.
"He had 45 minutes at Arsenal and it probably wasn't the easiest but it was a great finish. Who knows, that could be a goal which saves us from relegation."