Abraham has been largely snubbed by Manager, Thomas Tuchel since the German replaced Frank Lampard at Stamford Bridge.
The German tactician currently prefers his countrymen, Timo Werner and Kai Havertz for the striking role.
But Chelsea is planning on spending big for a striker this summer, with both Erling Haaland and Romelu Lukaku on their wishlist.
Both strikers would cost the Stamford Bridge outfit upwards of £100m but Tuchel must raise cash first, with Abraham considered one of their most valuable assets.
The 23-year-old England international scored 18 goals in his first season in the Premier League with the club last term.
Abraham’s current deal expires in 2023, meaning this is the last summer of his contract in which Chelsea could extract a high fee for the forward.
Leicester City and West Ham are both said to be interested in Abraham.