The Scotland international was forced off in the 55th minute of the 4-1 defeat on Wednesday following a strong challenge from Dedryck Boyata.
However, the 27-year-old striker has reacted well to the knock and will make the trip to Anfield, although he has been unable to train in the past two days.
"Fletch is in the squad," said Sunderland head coach Gus Poyet. "He hasn't trained, but he is in the squad.
"Most sportsmen know that when you get that leg in the back and hits the nerve, it's quite painful.
"Of course, it takes a couple of days to get the pain away.
"It's still a bit uncomfortable, but because there is no injury, he'll be in the squad."
Defeat to City was Sunderland's fourth game without a win in the league, but Poyet insists his side should not be too downhearted.
"I don't think we need to repair anything but the idea is to keep believing," he added. "I think it was more of a dream that we were in a position not to lose any of these three games in a row.
"The players need to recover. They don't have time to complain or put themselves down – they need to go out there and take the opportunity to get three points.
"We need to be brave – that's the word we're going to use the most this weekend. We are going in there willing to play and make it difficult in both ways, offensive and defensive."
