The 23-year-old has fallen out of favour with the Blues since Thomas Tuchel's arrival in January, and the Englishman has been told he can leave the club.
The imminent arrival of Inter Milan's Romelu Lukaku to Stamford Bridge may have also accelerated Abraham's expected departure, with the Belgian having had the first part of his medical on Monday ahead of completing a club-record £97.5m move.
A potential switch to the Italian capital would see the former Aston Villa, Swansea City and Bristol City forward link up with manager Jose Mourinho, who was appointed as the club's new boss in May.
Abraham made 22 appearances across all competitions for Champions League winners Chelsea last season, scoring 12 goals and providing six assists. body check tags ::