Lampard is reportedly weighing up a switch to Premier League strugglers Queens Park Rangers, now coached by former-Spurs manager Harry Redknapp, and Chelsea are thought to be looking to Bosnian international Pjanic as a long-term replacement.
The 22-year-old is currently playing in Serie 'A' for Roma, and is reportedly valued at £14m by the Italian club. The Daily Mail quotes sources from the Sunday People, which suggests Pjanic could move to Stamford Bridge if Lampard decides to end his association with the west London club.
Lampard started Chelsea's 1-0 defeat to Corinthians in the Club World Cup final, but the 34-year-old was left out of their semi-final victory over Monterrey - Rafa Benitez instead opting to play David Luiz in a midfield role.
Earlier this month, Lampard appeared resigned to leaving the Stamford Bridge club - his contract expires at the end of the season - and Rangers boss Harry Redknapp is looking for experienced heads to strengthen his squad when the transfer window opens in January.
He could turn to Lampard, his nephew, but many fans would be disappointed to see the Chelsea legend leave the club.
The England international has won three Premier League titles, four FA Cups and one Champions League trophy during a 12-year stint at Stamford Bridge.
His potential replacement, Pjanic, moved to Roma from Lyon in 2011, but has been linked with a Premier League switch in the New Year.
The attacking midfielder is rated as one of his country's brightest prospects, and the 22-year-old already has 37 caps for his country.