Dzeko has been strongly linked with a January move to Serie A, and Pjanic has been asked whether his friend, and fellow Bosnian, could join him in Italy.
"Will Dzeko transfer to Italy? I'm in contact with him and I know he aspires to play more and feel more important (than now)," Pjanic told Sky Sport Italia.
"He is a great player and he could do well in Italy but for now he is a City player, even though I don't know how long he will remain there."
Meanwhile, Pjanic says his Roma side are firmly focused on a top-four finish in Serie A this season.
"We will continue on our road to chase Juventus, a side who are having an incredible season," the midfielder told Mediaset.
"Our target is to return to the Champions League, then we'll see what we can do and what the others, especially Juventus, are capable of.
"But I am certain that we can finish the campaign in the top three."