The former England boss was due to speak at 14:30 CET to preview Monday's Premier League game away to Everton.
"Everybody at the club sends their best wishes to Roy for a speedy recovery," Palace said.
British media reports have suggested Hodgson is about to be sacked by Palace, who are currently 15th in the Premier League table and five points above the relegation zone, with ex-Eintracht Frankfurt manager Oliver Glasner tipped to take over at the south London club.
Hodgson, took charge of his 200th match as Palace manager earlier this week but his side were beaten 3-1 at Selhurst Park by London rivals Chelsea.
Palace have won three league games since beating Manchester United at Old Trafford in September and have lost 10 of their past 16 top-flight matches.
Hodgson, a boyhood Palace fan, is in his second spell in charge at Selhurst Park after returning for the final 10 games of last season when he signed a short-term deal to take over from Patrick Vieira.
He guided the Eagles to an impressive 11th-place finish in the table before agreeing to continue as manager for the 2023/24 season.
But recent weeks have seen supporters displaying banners calling for the much-travelled and vastly-experienced Hodgson to be sacked, with fans also venting their anger at the Palace board.
