Hodgson was forced to depart training with an undisclosed issue and his press conference which was set for 1:30pm had to be cancelled.
The fears around Hodgson's health come amid rumours that the club have already agreed terms with his replacement, as Oliver Glasner is reportedly set to take charge.
Hodgson is the oldest manager in Premier League history at 76 years of age, but his reign in charge at Selhurst Park looks likely to end imminently.
His illness may affect the timing of the club's announcement though, as their social channels have been less active, only posting updates on the manager's health.
At 12:55pm on Thursday, Palace's official Twitter account posted: «Unfortunately, today's press conference will no longer take place as scheduled as Roy Hodgson was taken ill during this morning's training session.»
Shortly afterwards later in the afternoon, a second update from the club arrived directly from their official Twitter account.
«Following news that Roy Hodgson was taken ill during today's training session, we can confirm that he is now stable and is currently undergoing tests in hospital. Everybody at the club sends their best wishes to Roy for a speedy recovery,» the statement read.
German journalist Florian Plettenberg claims that Palace are ready to hire former Eintracht Frankfurt boss Glasner as manager, following a run of just four wins in 18 under Hodgson.
After a late 3-1 defeat to Chelsea on Monday, Palace remain in danger of being sucked into the relegation picture, and they have two crucial fixtures on the horizon, starting with a trip
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