Per Sky Italia, Roma approached the former Arsenal and Chelsea midfielder as they step up their search for a successor to Claudio Ranieri.
Ranieri, 73, is set to retire from management now that the season is over and take a senior advisory role at the club.
Roma are yet to announce who will replace him and Fabregas, 38, has ruled himself out of contention, preferring to stay with Como.
Fabregas had also been linked with a move to Bayer Leverkusen before they settle on brining former Man United boss Erik ten Hag.