The Black Cats agreed a reported £14m fee with Liverpool for the striker, who spent last season on loan at the Stadium of Light.
There were suggestions that the delay could be down to Borini's reluctance to join the North-East outfit, but Poyet has insisted that this is not the case.
"I cannot tell you everything because it's not fair on anybody," Poyet told reporters in today's press conference. "But it's not like Borini doesn't want to come and we're trying to convince him. So calm, please!"
Borini scored 10 goals for Sunderland last season.