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The 21-year-old scored 26 times during a loan spell with Aston Villa last season before returning to Stamford Bridge to become Frank Lampard's first-choice centre-forward.
Abraham still has three years left to run on his £50,000-a-week contract that he penned before joining Swansea City on loan in the summer of 2017.
However, according to The Guardian, the Blues are keen to offer the striker fresh terms on a five-year deal - potentially doubling his current pay packet - following a strong start to the season.
The academy product made his Champions League debut against Valencia on Tuesday night but could not prevent Lampard's side from suffering a 1-0 defeat.body check tags ::
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