The Guardian reports that the Blues have opened talks with the striker, as well as his team-mates Fikayo Tomori and Callum Hudson-Odoi, over new five-year deals.
Abraham, who scored a hat-trick against Wolves last weekend, will more than double his current £50,000-per-week wages with the extension.
The 21-year-old has scored seven goals in his last four games under Frank Lampard after spending last season on loan at Aston Villa in the Championship.
Defender Tomori has broken into the Chelsea first team this season, and netted his first goal for the club in the 5-2 victory over Wolves. He will also be rewarded with a new deal with his current contract due to expire in 2021.
The report adds that 18-year-old winger Hudson-Odoi is closing in on a new five-year deal worth more than £100,000 a week as he edges towards a return from injury. Negotiations have been ongoing for months, but the winger looks set to sign on the dotted line soon.
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