Arsenal and Everton both appeared to be likely destinations for Zaha at different points in the transfer window, and the 26-year-old reportedly handed in a transfer request the day before the window shut.
A move failed to materialise, but the Ivory Coast international has handled the situation well, according to Hodgson.
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“With Wilf, I don’t think anyone was thinking we definitely must block him because we want our best player still with us,” the former England manager said.
“We understood that if a really big offer comes his way and a much bigger club than Crystal Palace want him, and he is desperate to go, we are going to have to try and do some kind of deal.”
Palace had placed an £80 million evaluation on Zaha, but no suitor matched that sum, according to Hodgson.
“The unfortunate thing for Wilf is that offer did not come his way from the sort of club that he would want,” he said.
“I think [Palace chairman] Steve Parish has made that clear to Wilf and they’ve thrashed that side of it out.
“As a result, it is not a major problem for me with Wilf coming back, having accepted the situation. The way he works here is just the same as it was. Since the first day, he has been mature about it.”