The 27-year-old Scotland international has missed the last four games with an ankle injury, but Poyet hoped to have him available for the final few games of the club's fight for top-flight survival.
However, after weeks on the sidelines, the prospect of the Sunderland star being able to make a return to action during the final month of the campaign looks increasingly remote.
Poyet said: "He's still injured and I don't think he is going to be a possibility now. I have been changing my mind about that because we were trying to push it, but we need to be realistic as well."
Fletcher has not featured since limping off at half-time against Crystal Palace on March 15, and Sunderland have lost all of the games they have played since, leaving them staring relegation to the Championship in the face.
The Scot, who was Sunderland's leading scorer last season, has managed just three goals to date during the current campaign.