The Belgian midfielder was understood to be Conte's top transfer target as he looked to overhaul a squad which finished the season in tenth place.
But Roma refused to sell the highly-rated midfielder and Chelsea turned their attentions to N'Golo Kante, who had spearheaded Leicester's surprise title win.
And the Frenchman has been a revelation for the Conte, taking them to the verge of their second Premier League title in three years.
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However, things could have been different had Nainggolan moved to Stamford Bridge instead of Kante.
And the 28-year-old says Chelsea were desperate to sign him.
He told Sky Sports: "Yes. I talked to him.
Radja Nainggolan was a target for Chelsea
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"They were really interested and wanted me over there. That's all I can say."
Nainggolan has enjoyed an impressive season for Roma, scoring 10 goals in 23 games.
And with reported interest from Manchester United and Arsenal, the midfield ace refused to deny a move to English football was not possible.
Chelsea boss Antonio Conte
"I watch it a lot,” Nainggolan added.
"A lot of my team-mates play there. It's the best league in the world.
"We have to make choices in life. I am having a good season. When the window opens we will talk about it again."