Calhanoglu has established himself in the Bayer side over recent years, capturing attention with some remarkable free-kicks, and has been widely linked with a move away from the Bundesliga.
"Barcelona and Manchester United are huge clubs. It would be difficult to turn them down but I have not said anything about any transfers or anything of the sort," he told Turkish broadcasters Lig TV.
The 21-year-old also acknowledged his head would be turned if Champions League holders Barcelona made a move, but says any talk of a move to Camp Nou is just speculation.
"I have not said anything and there is nothing to talk about, but of course if Barcelona made an offer I would have to consider it," Calhanoglu added.