The 25-year-old has impressed for Palace this season, scoring four goals and registering an assist in 14 Premier League starts. His side have never lost a game whenever he has found the back of the net, which was crucial for them to move out of the relegation zone.
Zaha's form has seen him attract interest from the top clubs in England. According to the Mirror, Pep Guardiola's side, along with the Premier League winners and the north London side were looking at the option of signing the Ivory Coast international. He is believed to be valued at £40m ($54.1m).
However, the former England manager has ruled out any possible sale of Zaha in January. Hodgson also stressed that his side are looking to further strengthen the squad in the mid-season transfer window.
"I have assurances from the club owners and Chairman, Steve Parish, that is not going to happen. We want to keep all the players we have got and ideally want to add to the squad in the January transfer window to strengthen even more," Hodgson said, as quoted by the Evening Standard.
"We are not too concerned about any rumours which might circulate because he is going nowhere.
"Wilfried has been absolutely excellent for us in this recent goodrun we have had and of course he is the iconic Crystal Palace player having been with us for so many years and being a local hero.
"He is doing everything he can to try and keep us out of the relegation zone and he is going to have to keep producing those type of performances for many more games because we have a long fight ahead of us."