The England international took Serie A by storm after leaving Chelsea in the summer of 2021, scoring 27 goals in 53 matches across all competitions during his debut season.
Abraham fired Roma to Europa Conference League glory with nine goals in the tournament, while he found the back of the net 17 times and provided four assists in 37 Serie A games.
However, the 25-year-old has failed to replicate such prolific form in the early stages of the current campaign, coming up with just four goals and two assists in 20 matches in all competitions.
Abraham was dropped to the bench when Jose Mourinho's side played Sassuolo on November 9, although he scored as a substitute before failing to fire once again versus Torino at the weekend.
When asked by reporters about Abraham's struggles last week, Mourinho suggested that the striker was too preoccupied with earning a World Cup spot for England, responding: "You should ask him what's the problem. If he is distracted, if he has a problem or if he's thinking about the World Cup.
However, Abraham was ultimately not selected for the England squad for the 2022 World Cup, and Calciomercato claims that Roma could be open to a sale in January.
The report adds that the Giallorossi will consider suitable offers for the ex-Chelsea man over the winter, with Tiago Pinto keen to raise funds to improve other areas of the field.
Abraham - who is not due to become a free agent until 2026 - has totalled 31 goals and eight assists in 73 games for Roma and is understood to be a target of Man United.
The Red Devils are on the hunt for a new number nine to replace Cristiano Ronaldo, who has seemingly played his last game for the club following his explosive interview with Piers Morgan.
England boss Gareth Southgate opted to take Callum Wilson to Qatar rather than Abraham, but Roma chief Pinto has criticized the 52-year-old for leaving the striker and Chris Smalling at home, as well as AC Milan defender Fikayo Tomori.
"I cannot accept, both Roma and the representatives of other clubs, that people try to justify international call-ups with what is happening at club level," Pinto told DAZN.
"If Tammy is not part of the England squad because he didn't score over the last month, for example, but they called up a player who was on the bench for his club yesterday, then in that case Smalling ought to be a starter for England.
"I want to say we are satisfied with Tammy, but always with the perspective that he can still improve, and I am sure he will do.
"We're pleased to see our players go to the World Cup, because it is important for them, but I cannot accept that after a call-up there is talk about the way these lads work at Roma as justification for a personal choice."
Last month, Abraham was quizzed on a possible return to the Premier League but insisted that he was "happy" with life at the Stadio Olimpico.