The 24-year-old was also linked with a move to Arsenal as the two clubs look to reinforce their backline with the addition of the centre-back.
However, the Serie A giants are prepared to hand him a new deal into order to ward away interest for the services of the former Olympiakos star.
The Blues are currently in the market to sign a long-term replacement for captain John Terry as he is expected to leave Stamford Bridge after being refused a contract extension.
Roma want to ensure Manolas rejects an offer given that they have already lost star defenders such as Marquinhos and Medhi Benatia, who joined Paris Saint-Germain and Bayern Munich respectively.
The Greece international has already featured 36 times in all competitions for his side this term, so far managing to score one goal while providing another two assists.