The winger’s form has lifted the Selhurst Park outfit out of the relegation zone to place 14th in the English top-flight log after a dismal start to the 2017-18 season - that coincided with his absence due to injury.
While being questioned of any certainty the former Manchester United flop would stay beyond the winter, the Englishman stated that he is unsure.
“I don’t think as a manager you can ever give guarantees on anything,” Hodgson said ahead of their trip to Swansea City.
”It’s a great credit to the club and Zaha that there are rumours circulating about so-called bigger clubs thinking about making a bid.
”If the day comes when one of those rumours are no longer rumours, I’ll come to terms with it and deal with it.
“Of course I do [want him to stay]. I‘m very happy with the way he’s playing and I have no doubt that will continue until the day when he can no longer do it for us. Like most Palace fans, I hope that’s a long way off.”
Zaha has contributed four goals in 12 English top-flight matches and will hope to continue when the Eagles visit the Liberty Stadium to tackle struggling Swansea on Saturday.