Hodgson accepts Cousin is in "some sort of limbo" with his proposed move from Rangers referred to FIFA - but maintains the £3million deal is "still alive".
Gabon international Cousin, 31, had arrived at Ibrox in early August from Lens, whom he played in both a French league game and Intertoto Cup match.
Hodgson insisted: "Yes, it is still alive. FIFA have requested further documents and I believe that one of their important executive committee members, who chairs the necessary commission which looks into these things, will consider the case on his return from the African Nations Cup.
"Hopefully then, we will get an answer - hopefully positive, but, even if it was negative, at least we would know where we are. But, at the moment we are awaiting that decision. Will it be next week? I don't know. FIFA have not yet said, we have not been told a date."
Hodgson continued: "I am more disappointed for Daniel Cousin, because he came here in good faith, and we took him here in good faith, and Rangers reluctantly agreed to sell him to us. And then, all of a sudden, because of this 20 minutes he finds himself in some sort of limbo.
"I'm still in contact with [Rangers boss] Walter Smith - we've been going past each other for two days, leaving voice messages - but I will be in touch with him, to find out what he thinks about the situation, and what the next move is."
Ultimately, though, Hodgson admits there is little either party can do, as the final decision now rests with the game's world governing body.
He said: "I suppose you could say it's frustrating, but, things you have no control over, there's not a lot of point in really letting them frustrate you. We don't control FIFA commissions and FIFA dates when they look at things, FIFA do.
"All we can do is ask them when that date is and they will give us the answer."
Hodgson, however, sees no reason why the deal should not be allowed to go through should FIFA give the green light.
"It's retro-active, if it's ratified, yes, he can play for us," insisted the Fulham manager. "We've done all of this within the transfer window, and if the appeal is heard, it's a bit like the Benjani situation between Manchester City and Portsmouth."