The Bosnian international playmaker has been linked with a host of Europe's top teams, with Tottenham Hotspur supposedly leading the Premier League interest and Borussia Dortmund hoping to recruit him as a replacement for Mario Gotze.
Pjancic, 23, has suggested that he may remain with his current Serie A employers beyond this summer, but also revealed that a move to Madrid or Barca would appeal to him when he feels that the time is right to leave.
"I have been a Real Madrid fan since I was a boy," Oslobodjenje quotes Pjanic as saying. "Certainly, this is my favourite club.
"Barcelona? Who wouldn't like to play for them? I feel good at Roma, though, and at this point I don't know if I'll leave this summer."
It has been reported that Barcelona are preparing an €11m (£9.4m) offer for the attacking midfielder.