Abraham has scored 30 goals in 82 appearances for Chelsea in all competitionsRoma's general manager Tiago Pinto arrived in London on Wednesday in an attempt to complete the signing of Chelsea striker Tammy Abraham.
Reports suggested the Serie A club, managed by former Chelsea boss Jose Mourinho, have already agreed a deal with the Champions League holders, although BBC Sport has not been able to confirm that.
But Roma are set for further talks with a view to signing 23-year-old, who has two years left on his contract and is still considering his next move.
Arsenal are also interested in signing the the England international, who was Chelsea's joint top goalscorer in all competitions last season with 12.
Abraham was rarely used after Blues boss Thomas Tuchel took over midway through last term and with Inter Milan forward Romelu Lukaku set to return to Stamford Bridge, playing chances could be further limited.
The expected £97.5m deal for Lukaku has created a domino effect, with Inter now linked with Roma forward Edin Dzeko as the Belgian striker's replacement.
In turn, potentially losing Dzeko has sharpened Roma's interest in Abraham.
But it is also understood that Pinto, who helped land fellow Portuguese Mourinho in May, is pursuing other options should Abraham decide to stay at Chelsea.
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