According to Adrian Kajumba of the Daily Mail, Chelsea are interested in the winger, who is valued at £80 million by the Eagles. Zaha handed in a transfer request in the summer amid interest from Arsenal and Everton, but neither club were willing to meet Palace's demands.
Per Sky Sports' Blake Welton, Hodgson said:
"Wilfried Zaha is not for sale so I don't need any assurances [from the board]. We are not trying to sell Wilfried Zaha. We want to keep Wilfried Zaha.
"But what assurances can people give? I suppose I have the assurance there is no-one at the club anxious to sell Wilfried Zaha.
"Of course, you never know where bids are going to come from and I suppose every time there is a serious bid for one of your players the board of directors need to take it seriously."
Chelsea wingers Pedro and Willian are both out of contract at the end of the campaign, so bringing in a new wide player to compete with Christian Pulisic and Callum Hudson-Odoi in 2020 would be a logical move.
In terms of dribbling, only former Blues star Eden Hazard could match Zaha when it comes to beating Premier League defenders in recent years:
His pace and skill on the ball have made him Crystal Palace's primary attacking threat, he draws a great many fouls, and he's often the difference-maker for the team:
Alex Goldberg of the CalcioLand Podcast isn't convinced the Ivory Coast international produces such moments often enough, though:
The 27-year-old has scored just three goals this season as well as contributing just two assists.
At Chelsea, he'd be expected to contribute a great deal more than that, particularly if the club pay the kind of fee Palace want for him.
It's not easy for him to be much more productive at Palace, though. Hodgson's Eagles are a defensive side who don't enjoy much possession or create much going forward—only Watford have scored fewer than their 18 goals this season—so Zaha is often an isolated figure left to do everything on his own.
Surrounded by better players in a more attacking team like Chelsea's, it's likely he'd be more prolific with goals and assists.
Zaha is the Eagles' most important player, and he's contracted at Selhurst Park until 2023. Palace are under little pressure to part with him in the middle of the season, so it will be difficult to negotiate a lower price for him.