Dzeko himself has been linked with a move away from City, but he's still keen for his Bosnian teammate to make the Premier League switch.
Pjanic moved to Roma from Lyon, and the 23-year-old is rated as one of the brightest young attacking midfielders in Serie 'A'.
But he's moved to play down speculation linking him with a transfer to Roberto Mancini's side, insisting he's content with life in Rome.
Speaking to Mediaset, Pjanic said: "It is nice to hear that Edin has spoken well of me, but I have a contract here.
"Perhaps one day we'll get the opportunity to play in the same club side, but for now, I'm proud to be able to wear this shirt."
The former-Metz youth team player rose to prominence with Lyon, before eventually moving on to Roma in 2011. He has 39 caps for Bosnia, where he plays alongside Manchester City striker Edin Dzeko.
The attacking midfielder has made 20 appearances for Roma this term, but is competing for a starting spot with the likes of Alessandro Florenzi and Erik Lamela.
As a result, his minutes have reduced but he's still managed to contribute three goals and four assists in the league. He started against Lazio on Monday night during the 1-1 Rome derby draw.