The Blues are looking to sign talented defender Stones this summer, but have already seen an opening offer rejected. They are aware that they will have to increase their bid if they intend to sign the 21-year-old, and believe the offer of a player may sweeten the deal.
Moses, who spent last season on loan with Stoke City, could be that player, with his future at Stamford Bridge still in doubt.
He was not allowed to continue a spell with the Potters, and the Standard claimed that head coach Jose Mourinho could utilise him in the first-team squad this coming season.
However, it could just be that Mourinho kept him with the Chelsea squad for the exact purpose of offering him as a makeweight in any potential transfer deals.
There are no indications as to whether Everton want Moses, or whether they would sanction a deal for Stones involving a player exchange, but there is one Premier League team who are looking to sign the winger.
The Mirror have reported that Tottenham Hotspur are looking to bring him to White Hart Lane this summer, and they could hold an advantage over the Toffees as the 24-year-old wants to remain in London.
With all the speculation, it is unlikely that Moses will continue with Chelsea past this summer, and the Blues would be securing a great deal if they can offload him as a part-exchange for Stones.