The Scotland international has not played since January'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 seeks to seal its first major trophy since the FA Cup in 1973.
"If [Fletcher] had been on the bench and he could have played 20 minutes then we would have put him in," the Uruguayan told The Sunderland Echo. "But I didn't want to have that dilemma of making him play more than he should. You can always get another injury as the main striker.
"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.
"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."