Abraham played just 17 minutes of football in the final three months of last season and was left out of the Chelsea squad for the Champions League final.
The striker wants to move on from Chelsea and the club are also prepared to let him go in the ongoing transfer window.
Arsenal are weighing up making a move for the Chelsea forward as part of their transfer plans this summer.
But it has been claimed that the Gunners would prefer to sign him on a loan deal while Chelsea want to sell him.
The Blues have set a £40m asking price on Abraham and want to extract the full figure from his departure.
Any permanent move for Abraham would have to see Arsenal move on a few strikers from the squad in the ongoing transfer window.
The Gunners are prepared to sell Eddie Nketiah and Alexandre Lacazette, who both have 12 months left on their Arsenal contracts.
They have offered Nketiah an extension but are willing to sell Lacazette whose departure could pave the way for Abraham to join.
The Chelsea striker is aware of the interest from Arsenal and would be open to a switch to the Emirates.
