The Daily Mail says Palace have held tentative internal discussions about the government's plans for over-70s in the wake of the Coronavirus pandemic which will affect their Hodgson.
Prime Minister Boris Johnson urged a number of groups including the over-70s will have to avoid all unnecessary social contact.
Hodgson is the Premier League's oldest manager aged 72 and would be impacted by any restrictions brought in by the government.
But with nothing concrete restrictions formally announced yet and doubts remaining about whether the season will even continue after last week's suspension until April 4, Palace can only monitor the situation closely for now.
Speaking earlier this month, Hodgson said: "Whatever decisions are made you have to abide by don't you, there's no question of that.
"We live in a democracy and we are all law abiding citizens.
"I'll worry about that when the time comes, but certainly I have never felt healthier and never felt happier about the environment I am in, in terms of health at a time when people are asking questions about the environment – I think I'm in the best possible place."