The Belgium international has reportedly been the subject of interest from a host of Premier League sides, such as Manchester United and Liverpool.
Roma have maintained they have no interest in selling one of their star men and though Nainggolan's representative expects him to stay, he admits Madrid could change things.
"I believe Nainggolan will stay at Roma, although when you are talking about Real Madrid, things can change," Ludovico Spinosi told IlSussidiario.net.
"[Roma president James] Pallotta knows that Nainggolan is very important for Roma and could have many offers for the player. Keep an eye out for Real Madrid."
The 27-year-old joined Roma last summer after spending four years at Cagliari and has three years remaining on his current deal.