The Blues tabled a £26 million bid for the Greece international but saw their approach immediately rebuffed by the Serie A outfit.
However, Roma have confirmed they would be willing to do business should the offer be increased to somewhere in the region of £35 million.
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A squad overhaul is needed at Stamford Bridge this summer amidst a poor defence of their Premier League title, with current manager Guus Hiddink admitting the club is in transition.
Chelsea are set to appoint a new boss before next season, with Italy head coach Antonio Conte's arrival seemingly imminent after the 46-year-old confirmed he will step down as national team manager after the European Championships.
Before his arrival, however, the Premier League giants want to make one or two quality additions for Conte to work with.
And it seems Manolas is top of their wish list, much like how several other European giants are chasing his signature.
Club legend John Terry is due to leave at the end of the season after being told his contract would not be extended for another year - therefore, the 24-year-old Roma centre-back could be viewed as his successor.
The versatile defender, who can also play at right-back, would add depth and quality to the west Londoners' ranks given his speed, strength and composure on the ball.