Borini impressed during a season-long loan at the Stadium of Light last season, scoring 10 times, and Poyet previously confirmed Sunderland had agreed terms over a reported £14million switch.
However, the 23-year-old cast doubt over the move when he joined Liverpool’s pre-season tour of the United States and his agent claimed he was planning on staying at Anfield.
After starting in the Reds' 1-0 defeat by former club Roma, Borini has since returned from America to receive treatment on a shoulder problem picked up in that game, which Poyet says has slowed the negotiations.
"He is being assessed now for his shoulder injury. That's stopped everything a little bit," Poyet is quoted in the Sunderland Echo.
"We will see. I have not held talks with him, but the club has, although that's private.
"We know where we stand."
Sunderland have already tied up a deal for former Chelsea full-back Patrick van Aanholt, as well as signing Billy Jones from West Brom, but Poyet has not given up on a move for Marcos Alonso, following his successful loan spell last season.
Reports have claimed that Fiorentina's price tag has deterred Sunderland from a permanent switch, although Poyet admits he would still be keen on securing the 23-year-old as he looks to add versatility to his defence.
"If you asked me before pre-season started, if I wanted two left footed left-backs, I would have said no," he said.
"Now if Alonso becomes on loan for free then we would probably take him. We need another full-back, the idea is one who can play right and left or with Billy (Jones) covering."