The 23-year-old has fallen out of favour under Thomas Tuchel at Chelsea and could be on his way out of Stamford Bridge at the end of the season.
Premier League duo West Ham and Leicester have been credited with an interest in the England international, who has scored 12 goals from 31 appearances for the Blues this term.
With the Irons and the Foxes interested in Abraham, Chelsea are prepared to part ways with the centre-forward, but are hoping to bank £40m for his sale.
Aston Villa forked out around £30m to sign Ollie Watkins from Brentford last summer and Chelsea feel they can demand £40m for Abraham, who has significant top flight experience under his belt.
Olivier Giroud is also expected to leave the London-based club in the summer and the departure of the two strikers will free up a significant amount from their wage bill.
Chelsea are also hopeful of raising funds through the sales of Kurt Zouma and Fikayo Tomori, who is likely to join loan club AC Milan on a permanent deal worth up to £30m.
Funds raised through the sale of fringe players will boost Chelsea’s bid to sign a top striker when the transfer window opens in the summer.
The Blues have been linked with moves for Borussia Dortmund star Erling Haaland, Inter striker Romelu Lukaku and Bayern Munich talisman Robert Lewandowski.