Incoming boss Antonio Conte is keen on the Belgium ace, 28, having twice tried to sign him when at he was Juventus boss.
Nainggolan last week revealed that international team-mates Eden Hazard, 25, and Thibaut Courtois, 24, have urged him to join them at Stamford Bridge.
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The midfielder, who has asked Roma to double his £60,000-a-week wage as an incentive to stay, admits he has discussed a possible move with Conte but says he wants to focus on the Euros before deciding his future.