Having spent time away from Stamford Bridge on loan, both youngsters will be told they must stay and fight for their place next season.
The Blues are set to serve a two-window transfer ban for breaching rules surrounding signing players under the age of 18, but have lodged an appeal with the Court of Arbitration for Sport.
However, The Sun claim that if the appeal is unsuccessful, both Abraham and Zouma will be told they must stay.
The England Under-21 striker has enjoyed a particularly fruitful spell with Aston Villa and his 26 goals have helped them reach the Championship Play-Off final.
Dean Smith is reportedly keen to buy or loan the 21-year-old if they find a way past the Rams at Wembley, but it is likely this will be rejected.
Similarly, France international Zouma has enjoyed a terrific season on loan at Everton. But with Gary Cahill leaving, the Blues will reject any offers for the 24-year-old.
Chelsea are in danger of having some of their best young players poached from them given their vulnerable position, with Reece James attracting attention after his great season at Wigan.
James has signed a new agent and is reportedly being watched by Crystal Palace – although there are a host of other clubs keen to sign the 19-year-old.
His parent club are adamant he will serve as cover for first-choice right-back Cesar Azpilicueta, but this is becoming more and more difficult.
Source: Talk Sports