For Sky Italia, Roma approached the former midfielder of Arsenal and Chelsea while driving up their search for a successor to Claudio Ranieri.
Ranieri, 73, will withdraw from management now that the season is over and a senior advisory role plays at the club.
Roma still has to announce who will replace him and Fabregas, 38, has kept himself out of the fight and would rather stay with Como.
Fabregas was also associated with a move to Bayer Leverkusen before they settle on the brining of the former man United Baas Erik ten Hag.