With veteran midfielder Lampard, 34, seemingly resigned to a departure from Stamford Bridge after 11 years with the club, Bosnia international Pjanic has emerged as a candidate to step into the former West Ham United player’s shoes.
However, the current European champions may face competition for the player’s signature from a familiar figure.
Former Chelsea manager Carlo Ancelotti, who was sacked by Blues owner Roman Abramovich moments after the team’s final game of the 2010-2011 English Premier League season, is also eyeing the midfielder for his Paris Saint-Germain side, according to the Daily Star Sunday.
Pjanic, 22, who is nicknamed The Little Prince by Roma supporters, began his footballing career with FC Schifflange 95 in Luxembourg after leaving Bosnia as a child following the outbreak of civil unrest in the country.
He joined French club FC Metz in 2004 aged just 14 and made his first-team debut in August 2007 against PSG.
Pjanic signed for Olympique Lyonnais a year later and, despite suffering a fractured fibula in October 2008, he went on to make 20 appearances in his first season at the club.
The midfielder rose to European prominence when his equalizing goal in the Champions League last-16 second leg knocked Spanish giants Real Madrid and Cristiano Ronaldo out of the tournament 2-1 on aggregate in March 2010.
However, after the arrival of Yoann Gourcuff at Lyon in August 2010, Pjanic was unable to find his way back into the first team and joined Italian club Roma a year later.
He scored three times in 30 appearances for the Serie A side last season and has been a first-team regular this term.
Pjanic has made almost 40 appearances for Bosnia since waiting eight months to make his international debut in 2008.
The midfielder’s Bosnian passport had expired and it was only following the intervention of Bosnian politician Zeljko Komsic that he was given a passport for his country of birth in early 2008.