The Scottish forward was put out of action after suffering an ankle injury last month, but Poyet admits that the Black Cats are still desperate to use him again in their fight against relegation.
"It's not looking good," the Uruguayan, whose side face Everton on Saturday, told reporters.
"We're trying our best to use him, whether it's possible for one, two or three games.
"I'm certainly not going to give up on Fletch but it's going to be difficult for him."
Sunderland are seven points from safety at the bottom of the Premier League table.