Zaha managed only four Premier League goals this season after pushing for an exit from Selhurst Park last summer.
And Hodgson insists Palace must make a decision on the Ivory Coast international.
"It's obviously affected him because his form in the last few weeks has really been quite poor considering what he is capable of doing," Hodgson told reporters after the season's conclusion, which saw Palace avoid relegation.
"It's a dilemma for the club and a dilemma for him if he is so set on leaving. If he feels he just does not want to be with us any more, that would be sad.
"We still like him very much; we can't make him like us. This is a situation that only he and the club can sort out. I don't have an answer."