That's according to the respected La Domenica Sportiva, which reports a fee of €46 million has now been settled between the two clubs.
Inter attempted to have United include Anthony Martial in their offer, but the English giants refused the demand.
Perisic has spent the weekend away from Inter's squad in Croatia, where coach Luciano Spalletti claimed he was visiting his personal dentist. The Nerazzurri also have dental surgeons on staff.
The midfielder has spent the past two seasons with Inter, arriving from VfL Wolfsburg.