The Italians had previously been claimed to want £66million for his signature.
But now, according to Calciomercato, an offer of more than £35m would be enough to secure his services.
That is just under half of the earlier figure reported by Italian newspaper La Gazzetta dello Sport.
And Calciomercato claim Abraham is top of Aston Villa’s list for attacking reinforcements.
Abraham, 25, previously spent the 2018-19 season on loan from Chelsea at Villa Park.
He helped the club secure promotion to the Premier League, netting 26 goals in 40 appearances for the club.
After scoring 27 goals in his debut campaign for Roma last season, Abraham has netted seven times so far this term.
Manchester United and Arsenal have both been linked with a move for the striker, as have former club Chelsea.
But another of Abraham’s former clubs in Villa are also thought to be keen on the attacker.
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Unai Emery’s side were previously linked with Abraham back in November.
And reports suggest Villa remain interested in his signature.
Roma are also said to be open to letting Abraham leave this summer.