The former Barcelona frontman has been struggling with a back complaint, but Hiddink believes he should be okay for the first leg of the last-32 tie.
"Yesterday [Tuesday] he trained fully. I think that he will be able to play tomorrow [Thursday]," the Dutchman said at a press conference.
The Russian Premier League is on a winter break, meaning second-placed Anzhi have not played a competitive match since Christmas.
Hannover have won two and lost two since they returned from the mid-season break, most recently a 1-0 win over Hoffenheim at the weekend.
But Johan Djourou knows that the visitors will have to be on top of their game to keep the likes of Eto'o quiet.
"Of course Samuel Eto'o is a serious threat," he said. "Everyone knows how he famously played in Barcelona and won many titles. It will be difficult against him."
Anzhi qualified in second place from a tight Group A, level on points with pool leaders Liverpool and third-placed Young Boys, while Hannover topped Group L ahead of Primera Division high-fliers Levante.
The big-spending Russians start as favourites, though, with the January signing of Willian for a reported 35 million euros from Shakhtar Donetsk the latest statement of their ambition.
They have lost defender Christopher Samba to English strugglers QPR, but goalkeeper Vladimir Gabulov feels they can cope without the powerful centre-back.
"It should not be a problem," he said. "We have someone to replace him."
And Hannover coach Mirko Slomka admits his side will have to battle if they are to secure a result to take back to Germany.
"We will do the work," he said. "We will try to surprise the opponents, who are of course, very, very strong. I can assure you that it will be a real battle."