The Italian club have already rejected two bids and are holding out for £31 million for the Belgian star.
A price that high would usually be enough to hold off any interest, but Chelsea have made signing Nainggolan one of their top priorities this summer, even though a move looked unlikely earlier this month after Roma coach Luciano Spalletti said that the Belgian had given his word to stay in Italy.
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However, it may only be a matter of time before the 28-year-old leaves Roma, as Chelsea are ready to step up their ruthless attempt to sign Nainggolan and make his current club an offer they can't refuse.
The Blues had a £27 million bid rejected earlier in June, so it's likely Roman Abramovich will stump up the extra £4 million to match Roma's price.
Incoming Chelsea boss Antonio Conte reportedly wants to pair Nainggolan with Leicester City's N'Golo Kante in his midfield next season. Kante himself has a buyout clause of £20m in his current contract, so bringing both of these players in would cost the Blues over £50m in total.
Both players are currently at Euro 2016 representing their countries, but Nainggolan has come under heavy criticism for his early performances in the competition.
He was dropped to the bench after a poor performance against Italy in Belgium's opener, but has since turned his fortunes around, and scored a stunning winner against Sweden.
Kante has had a better tournament, and after some brilliant midfield displays, he has become the first name on Didier Deschamps' team sheet, while becoming a fan favourite at the same time.
Both players will be hoping to inspire their countries to victory at Euro 2016 after both teams progressed to the quarter-finals over the weekend
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