The Italian giants are under scrutiny regarding Financial Fair Play and after missing out on the chance to play Champions League football next term, they may be forced to sell some top stars.
According to the Daily Telegraph, Roma will listen to offers for the striker as they look to cash in on the star.
Abraham joined Roma from Chelsea for a fee of £34million in the summer of 2021, with Jose Mourinho's side keen to recoup the majority of the fee paid for the player.
Interest will be high in Abraham's services this summer, with Manchester United and Paris Saint-Germain both having scouts watching the star this term.
Meanwhile, Chelsea may also be interested due to holding a buy-back clause on the England international.
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Abraham has scored 36 goals in 106 appearances for Roma, but says that he's enjoyed the chance to step up and become a key player for such a big club.
He told UEFA.com: "I've become more confident and have learnt a lot about myself.
"At Chelsea I was known as 'the academy player', and I think coming here I've realised it's time to bring out my personality and show the world what I can do.
"It's been an amazing experience learning about a different culture and seeing a different area of life.
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"It's something I'll treasure even more looking back when my career has finished."
Roma finished sixth in Serie A in the 2022/23 season, and their defeat to Sevilla in the Europa League final means they'll have to settle for a second straight season in the secondary European club competition.