Abraham lost his place in the Chelsea squad after German coach Thomas Tuchel replaced Frank Lampard.
With Romelu Lukaku set to join Chelsea, Abraham will have to look elsewhere for more playing time and a move to Roma would be the best option as their bulky striker Edin Dzeko edges close to Inter Milan.
Despite rumours linking Abraham to Roma, the England forward was added to Tuchel's squad that will face Spanish LaLiga club Villarreal in the Super Cup final on Wednesday.
Abraham was with Chelsea's youth side during Jose Mourinho’s era but never made a senior debut before the Portuguese gaffer left the side.
Speaking on the 23-year-old's potential move to Roma, Tuchel insisted he's responsible for the lack of opportunities had by the former Aston Villa man last season.
"Tammy is right now in the squad. He did some good preparation matches.
"He was clearly not happy with the last half a year and maybe he has reason also not to be happy and maybe it was also my fault not to push him, not to trust him on the same level I maybe trusted other players.
"I can absolutely understand that he wants more minutes. So the decision will be 'how do we plan, what are Tammy's plans, does he fight his way back into the team from the position where he ended last season or does he want to change club to have the chance of being a regular starter?'"
Abraham managed to register 12 goals in all competitions for Chelsea last season.
