The 29-year-old sustained the injury in last week's first leg in Germany, which ended goalless.
Hodgson insists he will not gamble on the fitness of Zamora and admits it will be touch and go whether the striker is available.
"Bobby is much improved and has done some work today with the physios, but we chose for him not to take part in the light training session we had," said Hodgson.
"We just have to wait until tomorrow to have a 100% decision on whether or not he can play.
"Obviously we are concerned about the situation, because if he was fully fit, he would have been training for the last couple of days."
Hodgson added: "When Bobby plays we know what we are doing, and when he does not play, we have people who come in and know what we are doing, so we can leave it late in that respect.
"He will have treatment again tomorrow, then go in front of our medical people, and I think by lunchtime I should know whether or not he has a chance of playing.
"It will be about their assessment, Bobby's own assessment, how he feels, how he thinks it will go - because knowing him as well as I do, he will not want to let the team down.
"He wants to play, but he wants to play as a fit player rather than play and in any way hamper our chances of doing well."
Right-back Chris Baird is suspended, so John Pantsil, fit again following a knee problem, is set to come into the side.
Cottagers manager Roy Hodgson reported no fresh injury problems, having rested some nine players for the Premier League trip to Everton.
Stefano Okaka and Nicky Shorey are both ineligible.
Kick-off at Craven Cottage is 8.05pm.
Fulham (from): Schwarzer, Konchesky, Hangeland, Pantsil, Hughes, Etuhu, Duff, Murphy, Gera, Davies, Zamora, Dempsey, Zuberbuhler, Nevland, Greening, Dikgacoi, Smalling, Kelly, Elm.