It's believed that Bennett has a clause in his contract with Lyon that frees him if they are relegated to the Second Division and while the Ospreys originally offered him an improved contract to stay at the Liberty Stadium, they are no longer in a position to do so.
And Ospreys forwards coach Jonathan Humphreys has confirmed Bennett will not be returning to the club, even though he'd be welcome in theory.
"We'd have loved to have kept Huw before this, but the simple fact is that financially we can't," said Humphreys.
"We certainly don't have the finance. That's unfortunate, but it's the case."