Spalletti is very fond of Vucinic as he was the one who brought the striker to Roma during his days their as coach and now wants him to join at Zenit.
And Juventus could be willing to sell the 29 year-old as they want some funds to fuel a move for fellow Montenegro striker Steven Jovetic who is currently plying his trade for Fiorentina.
Jovetic is also being watched by the likes of Arsenal and Chelsea so Juventus will need to act quickly before he gets snapped up.
Vucinic scored 16 goals and 10 assists from a total of 49 appearances in all competitions during last season.