The Bosnian has been linked with a move away from the capital in recent weeks, with the likes of Juventus and Inter both keen to land the 34-year-old.
However Fienga has thrown cold water on those reports by making it clear Dzeko remains a key figure at Roma.
“Dzeko is Roma captain and he will continue to be Roma captain for as long as he wants,” he told reporters at the Premio Calabrese Award ceremonies.
“The transfer market? I am doing a job that isn’t mine so you won’t hear me speak like a football expert. I help the club with negotiations while keeping costs in check.
“I think Roma have a strong coach and a strong squad, but we have to strengthen the areas where we are a bit thin.
“We have made a big effort since last year to try and keep the players that have shown themselves to be stronger, so we don’t want to let them go.”
Rumours have linked club legends Daniele De Rossi and Francesco Totti with a return in some shape or form under The Friedkin Group, and Fienga wouldn’t rule out anything.
“I take it as a given the passion that De Rossi and Totti have for Roma,” he added.
“It’s wrong to put pressure on them and think that they will return for certain. They are part of Roma’s history, but they’ve just begun their new journeys so time is on their side.”