"It was Wilf's first training session today," Hodgson told a news conference.
"It was debated whether he should join in, but he was determined to. We will have to see how tomorrow pans out before we decide how we play on Saturday."
Zaha's importance to Crystal Palace is underlined by the fact that they last won without him in September 2016.
They have failed to score in 10 of those 12 games, including last time out against Southampton.
"Until such time as we do win a game, Wilf can sit there knowing he is the man we need to play," Hodgson added.
Hodgson confirmed James Tomkins has recovered from his calf issue but striker Christian Benteke will be sidelined with a "niggling knee injury" which resurfaced on international duty with Belgium.
Palace have suffered three consecutive league defeats to Liverpool, Watford and Southampton since their 2-0 win over newcomers Fulham on the opening weekend of the season.
Despite scoring just three goals in four matches, Hodgson has backed his players to turn a corner at Huddersfield.
"We have played well against some of the top teams," he said.
"I don't personally subscribe to the theory we can only do it against the bottom teams. We have been close against the top teams, and we are capable of giving those performances."
David Wagner's Huddersfield are searching for their first league win in nine games after losing four and drawing four.
(Reporting by Hardik Vyas in Bengaluru; Editing by Toby Davis)
