The report claims the 29-year old could be allowed to leave after the club’s ongoing difficulties in tying him into a new deal.
The Bosnian's Contract runs until 2017 but he has been reluctant to accept the terms currently on offer by the Serie A giants and could go, despite his popularity with the club's fanatical support.
West Ham are in pole position, according to the report, but it remains unclear whether an approach would be made in January or next summer.
Lulic has been an ever-present for the Italian club since his move in 2011- scoring 15 goals in 122 appearances - and would be a shrewd acquisition for any of the Premier League clubs mentioned.
He operates primarily as a left winger but can drop into the left-back position if needed and the recent injuries to Tyrone Mings and Max Gradel for Bournemouth are cited as a possible reason for the Cherries’ interest.
Watford’s Italian connections could be key in facilitating a more but they have less of an urgent need with the loan signing of Roma left-back Jose Holebas.