Sterling can leave Stamford Bridge after the club made clear he has no future under head coach Enzo Maresca.
Blues officials have been working on identifying potential destinations for their £47.5million forward with Palace one of the clubs to have expressed an initial interest.
There are clear obstacles towards any successful switch to Selhurst Park, particularly given Sterling’s reported £325,000-per-week salary.
Mail Sport understands Palace are still trying to ascertain the exact conditions of a deal and whether it is realistic.
There are some obstacles to Sterling's Palace move, including his £325,000-per-week salary
But Eagles officials are keeping abreast of developments regarding the forward’s future ahead of Friday’s deadline.
Sterling’s future has come to a head in recent days after representatives for the player issued Mail Sport with a statement asking for clarity on his position after we got wind that the forward would be dropped from Maresca’s first squad.
The player has held direct talks with Chelsea, who have agreed to present Sterling with his options in advance of next week’s deadline, with a view to sorting his future.
Other than Palace, Aston Villa have a tentative interest but, similarly, a lot of obstacles need to be cleared for that deal to accelerate.
Juventus also have an interest and enquired about Sterling’s availability earlier this month.
Federico Chiesa’s potential move to Barcelona could open the door to Juve tapping up their interest in Sterling.
The 29-year-old’s family are settled in London following their move south from Manchester City in 2022 and Sterling is keen to avoid further upheaval for his children.
With that in mind Palace’s London location could enhance their chances of persuading Sterling to stay in the capital with them.