Poyet told the club's official website he is happy with the progress of the Scotland international, as he recovers from injury.
When asked if the former Hibernian and Wolves forward will be available for the weekend, Poyet said: "There is a big possibility. It's some of the very good news from this week.
"Every player is important but we know in football that there is a few positions that are key; the goalkeeper, the spine of the team and the main man up front scoring goals.
"We need goals; we need players who have got the ability and Fletcher is one of those players."
However, Poyet insists the backroom staff at Sunderland have to be cautious with the 26-year-old, who has suffered two long-term injuries in the past year.
"It's funny because we are trying to make him train as much as we can but without breaking him," Poyet added.
"We are nearly there and I'm sure he's also happy to be part of the team trying to get ready for Saturday."