Conte is now on course to win the Premier League title in his debut season on the Chelsea bench, as the Blues are four points up on Tottenham in the standings.
Nainggolan admitted that he spoke directly to Conte last summer, but Chelsea refused to match Roma's £34 million asking price.
The Sun claims that the Italian boss is considering a return to his home country to lure Roma stars Antonio Rudiger and Radja Nainggolan to Stamford Bridge.More news: Powell scores 25 as Raptors beat Bucks 118-93 in Game 5
In order to do that, they are willing to offer Conte or Atletico Madrid boss Diego Simeone a salary of €15m-a-year to oversee their success.
Rudiger was linked with a move to the Premier League last summer as well before a serious injury ruled him out of Euro 2016.
Nainggolan has always been linked with a move to Stamford Bridge and Conte is desperate for the midfielder to finally join the Blues and add some serious class to his side.More news: North Korea accuses US, South Korea of assassination attempt
However, with Chelsea captain John Terry set to end his illustrious career at the at the end of this season, the Blues will need a new centre back to take over from him and Conte feels the German is an ideal replacement.
Nainggolan is a key part of the current Roma side and played for the second placed team in Serie A, for their win at AC Milan on Sunday night.
Check out some of Antonio Rudiger's best defencive work for AS Roma so far.More news: UFC boss Dana White believes Anthony Joshua saved boxing from 'dying'