Fletcher has not played since January 29's 1-0 win over Stoke City because of an Achilles injury.
The Scotland international returned to training last week but 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, however, the Uruguayan feels the former Wolves man could play a part as Sunderland seek to seal their first major trophy since the FA Cup in 1973.
"If he (Fletcher) had been on the bench and he could have played 20 minutes, then we would have put him in," Poyet 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."
Sunderland were comfortably second best against Arsenal, although the Wearside club did get a second-half consolation through substitute Emanuele Giaccherini.
That strike marked only the Italian's fourth goal of the campaign but, with goal difference a potential factor in Sunderland's fight against relegation, Poyet feels the effort could be crucial in the end of season shake-up.
"It's been difficult for Giacchy," Poyet 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."
