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.
And big Premier League teams such as Chelsea, Manchester City and Arsenal have made the player a target.
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.