Pjanic has been linked with a host of European clubs during the close season, despite new Roma coach Rudi Garcia lavishing praise on the Bosnian playmaker since his arrival.
Spurs have been monitoring Pjanic for an extended period of time and made an enquiry to the Giallorossi through director of football Franco Baldini, according to The Mirror.
Baldini, who worked at the Olimpico in his last job, reportedly called current Roma director Walter Sabatini to see if a deal could be done for Pjanic.
Roma are reluctant to sell the 23-year-old this summer, due to a widely-held belief in the Italian capital that Pjanic's best years lie ahead.
Since joining Roma in 2011 Pjanic has played 60 times in all competitions, while also earning 41 international caps for Bosnia and Herzegovina.