Shaun Wright-Phillips insists he is happy again at QPR after turning down "offers and opportunities" to move in January.
Blackburn goalkeeper Paul Robinson has told Sky Sports he will leave the club this summer and could move abroad.
The 22-year-old is a natural right-back but filled in for injured left-back Danijel Pranjic during Croatia's World Cup campaign in Brazil and has previously played in midfield.
A statement published on Sassuolo's official website said Vrsaljko would be presented to the media at 1430 BST on Wednesday.
The Neroverde have already added Federico Peluso from Juventus, striker Antonio Floro Flores and midfielder Davide Biondini to their ranks as they look to consolidate their position in Serie A having narrowly secured survival at the end of their maiden top-flight campaign.
Sassuolo have also on Wednesday confirmed the departure of 23-year-old midfielder Karim Laribi to Serie B side Bologna on a season-long loan.