The Eagles are currently 17th in the table after winning just three of their 13 games in the top flight.
The club are only out of the relegation zone due to a better goal difference than Hull City, but the current predicament has sparked concern over Pardew's future at the club.
The 55-year-old has claimed that he has the support of chairman Steve Parish and the rest of the board, but it is believed that a contingency plan is in place if the club opt to part ways with Pardew.
"The chairman and the board here have been fantastically supportive," Pardew told reporters in Friday's press conference. "This is a great football club and one they have great plans for, but it's in crisis at the moment, a kind of mini-crisis, and we need to get through that.
"The work they've done, what they want to do going forward, all bodes well. But we have to get past this period. He just really wants to see us putting the effort on the pitch at a level where we can get a result."
Palace will welcome Southampton to Selhurst Park this weekend in a bid to bounce back from their 5-4 defeat to Swansea City.