The Premier League side are prepared to spend big to land the Belgium midfielder and made an approach for his services earlier this summer.
Nainggolan has now confirmed he spoke to new Blues boss Antonio Conte before travelling to France for Euro 2016.
But he says talks have stalled and that he has now told Roma’s president he is ready to stay with the Serie A club.
Nainggolan said: “I said to him I love where I am playing so why not stay?”
The midfielder scored Belgium’s winner against Sweden on Wednesday to set up a last-16 game against Hungary, and Conte knows all about him from Serie A.
They were in talks last month, but Nainggolan said: “Chelsea were talking but at the moment there is nothing.
“The Premier League is a big competition, it’s lovely, but I think sometimes in life you need to make choices, and all I can say is that I am happy where I am.”