The midfielder was the subject of an offer from the Premier League side but he has promised to stay in the Italian capital after talks with Walter Sabatini.
Radja Nainggolan has insisted that he has no intention of leaving Roma amid ongoing speculation he could depart the Serie A side for Chelsea.
New Chelsea manager Antonio Conte is a keen admirer of the combative midfielder and had been hopeful of luring him to Stamford Bridge.
The Belgium international confirmed there had been contact between the two clubs, with Goal learning in April that a deal had been struck.