Moses is the first casualty of Maurizio Sarri's overhaul of the squad at Stamford Bridge after failing to impress the Blues boss.
SunSport revealed exclusively earlier this month that Chelsea were looking to cash in on the Nigeria star when the transfer window opens in January – with Palace at the front of the queue.
Wolves and West Ham had also registered an interest as the look to bolster the squads mid-season, but it is the Eagles who look to have won his signature.
Palace are confident they have a deal in place to take the 28-year-old back to South London, where he began his career after coming through their academy.
He left to join Wigan eight years ago before making the move to Stamford Bridge for £9m in 2012.
Moses then spent loan spells with Liverpool, Stoke and West Ham before finally establishing himself as a Chelsea player under former boss Antonio Conte.
He became a regular part of Conte's starting side operating as right wing-back, helping the club to Premier League success.
But Moses has been unable to convince new Blues boss Sarri that he should be a part of his long-term planning for the club.
So he becomes the first player shipped out by the Italian as he looks to make his own mark from the squad he inherited on the eve of the new season.
Another one who could be sold is striker Tammy Abraham, who is currently impressing in a loan spell at Aston Villa.
The England striker is due to spend the whole season at Villa Park, but Chelsea have the option of recalling him in January in the contract.
And they are considering cashing in on the 21-year-old, with Newcastle showing an interest in securing a permanent deal.
Newcastle tried to sign him on loan 18 months ago but Swansea secured the deal instead, and the interest is there to come back with an offer if he become available.
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