Jordan Ayew and goalkeeper Sam Johnstone penned new deals at Selhurst Park this week, and Hodgson says the wheels are in motion for Eze to do the same.
The England international signed for Palace from QPR in 2020, but has been out with a hamstring injury for a month. He is out of contract in June 2025 as it stands.
"We had the good news with Michael Olise earlier on in the year, now those two", Hodgson said of Ayew and Johnstone's contracts.
"I believe the club are working very hard with Eberechi Eze. And I think they are fairly confident that it won't be too long before the club can announce him too.
"These matters are taken care of by [chairman] Steve Parish and [sporting director] Dougie Freedman. They keep me informed, and I don't have any impact on that. But certainly they are optimistic that it won't take too long to get Eberechi to commit his future as well."
Eberechi Eze is set to sign a new Crystal Palace contract
Providing an update on Olise and Eze's hamstring injuries, Hodgson said: "Both are making good strides. We've had the benefit of Ebs being released to us this week, so he's taken part in training pretty much as normal.
"Michael Olise is making good strides, but these sports science people are a little more careful with him. So they haven't released him to us to the same extent. But he has taken part in parts of the training session, and he's looking good, and I'm pretty hopeful that next week he will be - like Eberechi Eze - released to train fully with the group.
Asked when they will return to the team, Hodgson said: "Before the international break, both of them, without a doubt. Hopefully even for the Everton game - it's not out of the question.
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"It will depend to some extent how both of them deal with the week's training. In Ebs's case it will be two weeks' training, and in Michael's case it will be one week. [James] Tomkins is getting close now, and Dean Henderson is still working through his injury as well."
Hodgson was criticised after Friday's defeat to Tottenham for saying young substitutes Jesurun Rak-Sakyi, Matheus Franca and Naouirou Ahamada had made Palace "weaker" when they had come on. Franca is 19, while the other two are 21.
"It was wrong of me to do so in the disappointment of the game", Hodgson said of those comments.
"I think it's very unfair and wrong of me to expect more from them from that game. I've spoken to them about that.
"We are happy with them, we are happy with their development, and they are getting better and stronger all the time. The young players we've got are good ones - and they will become very good ones."
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