The Champions League semi-finalists will demand a fee of around £40million for the 23-year-old, who has fallen out of favour following the arrival of new boss Thomas Tuchel at Stamford Bridge.
Abraham scored 26 goals while on loan at Villa during the club’s 2018-19 promotion-winning season and still has plenty of admirers inside Villa Park.
Villa are thought to have explored the possibility of signing him permanently the following summer but Chelsea were not interested in selling him at the time.
Abraham has since gone on to prove his Premier League pedigree by scoring 31 times over the last two seasons, including a first senior England goal.
Leicester and West Ham are among the clubs also reported to be monitoring his situation and there is expected to be no shortage of interest in his signature both in England and on the continent.
Villa’s focus during the next transfer window will be on bolstering their options in attack.
And while the priority is on adding pace in wide areas and recruiting a No.10 to ease the burden on Jack Grealish, Abraham’s situation will also be monitored.