Initial diagnosis from a London specialist indicated Beye would face an operation to repair ankle ligament damage, but Beye jetted out to Marseille last week to receive a second opinion on his injury from a specialist.
Kinnear Faces 'Worst Nightmare'!
The problem could clear up within 10 weeks with physiotherapy.
Kinnear (talking to the Chronicle): "It would be a nightmare if Habib was out for the rest of the season.
"We just have to wait and see.
"People talk about the need for getting a replacement, but it is difficult to replace quality players just like that.
"Habib is like a captain in many ways.
"He is an automatic choice when fit, not just because he is a great player but also because he is a good organiser at the back.
"You knew you were missing an organisational player like Habib in the Liverpool game when we were cut to ribbons.
"He is great in the dressing room - and we are missing him right now."