The young winger was a reported target for the Serie A giants but has opted to extend his current contract with the Ligue 1 side until 2019
The Giallorossi were reportedly keen on bringing the Belgian to Stadio Olimpico and are believed to have tabled an offer potentially worth €6 million for the 20-year-old this summer.
However, Ferreira-Carrasco has instead opted to sign a new deal to tie him to the Ligue 1 side until 2019.
"I'm very happy to be a part of the ambitious project of AS Monaco," he told the club's official website.
"The extension of my contract is a real sign of confidence on the part of the coaches and management. And the chance to compete in the Champions League with my formative club is a source of pride."
Monaco vice-president Vadim Vasilyev was keen to stress that retaining Ferreira-Carrasco was a sign of "the importance of youth in the project" at the club and admits there was significant interest in the former Genk winger.
"Yannick won the Coupe Gambardella (Under-19 tournament) with Monaco [in 2011] and this season he will defend the colours of his formative club in the Champions League.
"He was pursued by many clubs, but he has chosen to extend and we are very happy to see him join our project."