Palace forward Zaha, 27, is being linked with Spurs and Everton.
Hodgson, preparing for today's Premier League opener against Southampton, said: “There are a lot of things being said and a lot of people putting ideas into his head.
“So it's not the easiest thing for him to come to terms with.
“The external influences are quite great and he has to battle a few demons there.
"But I must say I'm basing my opinion on what he is doing at the moment.
“His training and the matches he has played for us, there has been no problem at all.
“You'd have to speak to Wilf to find out the exact state of his psyche — but I'm not concerned."
Hodgson has urged his star man to improve his displays if he has aspirations of moving on to a higher level.
The 73-year-old said: “I'm surprised we don't get more people knocking on our door who are willing to pay a sensible price for him because he's such a good player.
“He might get a bit frustrated sometimes that we aren't having to turn down offers every single day from some of the top clubs in the world.
“Because he thinks he has that ability to play there and I think so, too."