The Premier League pair have been linked with the Bosnian ace for some time, amid rumours that he has grown unsettled in Rome.
However, their hopes of achieving a deal for the 23-year-old may hinge on interest from PSG.
The French champions are believed to be watching the playmaker, and could launch a £20m raid before the end of the transfer window.
The Parisians can offer Pjanic a realistic chance of silverware both domestically on the continental stage, as well as a lucrative contract thanks to their Qatari backers.
Roma value their star at around £20m, which could make him a wise purchase ahead of the World Cup, where his performances may cause his value to increase.
Tottenham have been linked with Pjanic on a number of occasions over the past few transfer windows, while Liverpool are also thought to be interested as they search for a marquee signing.