Wales international Hennessey was forced off during the closing stages of the Nations League win in Bulgaria on Wednesday night, and the full extent of his upper thigh problem is still being determined.
Hodgson worked with Stoke keeper Butland during his time as England manager and admitted the 27-year-old was a potential target to bring to Selhurst Park.
“Jack’s name has been mentioned, obviously we are aware of the problems we would have if it turns out Wayne’s injury is a serious one which is going to keep him out for a longer period of time,” Hodgson said at a press conference ahead of Sunday’s Premier League match against Brighton.
“That would leave us very light on the goalkeeper front and certainly I know Jack’s name is one name which has been mentioned, but he has not been the only name mentioned.
“This is a job for our sporting director Doug Freedman, who is working hard to see what options are available and will then present them to me sometime this afternoon if he has been able to find an option.”
Hodgson also revealed Republic of Ireland midfielder James McCarthy was set for a spell out after picking up a hamstring problem while away on international duty, which is expected to sideline him for up to three weeks.
The former England manager added: “I’m not going to be saying anything other than it’s unfortunate.
“I believe it’s good for players to play for their national team and I believe they want to play and should be grateful every time they’re called up and given the chance.
“I’m quite sanguine about the fact that these things happen and I would not dream about complaining about the fact it has happened.
“I just feel very sorry for Wayne if it’s going to keep him out for any length of time because he missed the Euros this summer and was very anxious to get ready for the Euros next summer and now of course he has got this setback.
“He will have to get kicking on again as soon as he is given the green light to start playing.”
Hodgson was, though, left irritated by the impact on Cheikhou Kouyate of having gone away on international duty only for Senegal’s late call off of their home friendly against Mauritania just hours before kick-off because of COVID-19 infections in the visitors’ camp.
“There’s nothing much we can do about it, but one is concerned in a global pandemic that players are going to somewhere like Mauritania only for their game to be cancelled,” the Palace boss said.
Gary Cahill, James Tomkins, Patrick Van Aanholt and Jeffrey Schlupp have all stepped up their recovery during the international break and could be involved against Brighton.