Chelsea had a summer offer of €70 million rejected by Roma, according to club director Bruno Conti.
The 28-yard-old has previously been linked with Manchester United and Real Madrid.
However, Chelsea, not one of those clubs who have mentioned previous were revealed to have made a bid for the midfielder, by Roma's Conti.
"De Rossi will stay at Roma, no doubt about it," Conti told Radio Mana Mana.
"I would like to remind people of the following: Chelsea offered €70m for him, a lot of money, but [then president] Rosella Sensi turned it down."
The news of Chelsea's substantial bid being rejected will be bad news to potential suitors, such as United, who will have hoped to snatch the World Cup winner, for a cut price in the coming transfer windows.