Palace have been given the green light in principle to expand the capacity of their stadium from 26,000 to more than 34,000.
But the club are still in negotiations with Croydon council over the terms of their planning obligations, while Mayor Sadiq Khan needs to give his approval before final planning permission is issued.
And those talks with the local council are taking longer than expected, which could result in Palace having to push back the start date for work on the redevelopment.
Palace want work to start at the end of this season, with a view to the stand being ready for the beginning of the 2021-22 season.
Palace chairman Steve Parish, speaking to the FYP podcast, said: “There are final things to work out with the council. There are no problems, it just takes longer than we thought it would.
“We were hoping at the end of this season but it is drifting away from us slightly. Still, if we can make it happen, then we will.”
A spokesman for Croydon council said: “We continue to have productive discussions with Crystal Palace about the redevelopment of Selhurst Park.”
Meanwhile, Palace striker Christian Benteke has had knee surgery and is set to be sidelined until next month at the earliest.
In a statement, Palace said: “Christian has undergone minor arthroscopic explorative surgery and a washout of his knee, as it had not been settling with conservative management.
“The surgeon was happy with the outcome and we expect Christian to return to training very soon. A further update will be given in a few weeks’ time.”