Manager Steve Bruce has not completely ruled the former Manchester United reserve team captain out of the Wembley trip but admitted it is highly unlikely he will be fit in time.
The centre-half came off just before half-time against Aston Villa on Saturday and appears to have aggravated an injury that kept him out for 11 weeks between September and December.
"The earliest reports on James look as if the hamstring that he's come off with, he's re-injured it. It looks bleak for the lad," said Bruce.
"We can't say until we scan him and know the extent but it doesn't look very good for him."
Nigeria forward Sone Aluko is also sweating over his fitness after turning his ankle in training last week, as Hull prepare for Tuesday's trip to Manchester United.
"Sone won't be available on Tuesday, it's touch and go for the cup final I'd have thought," said Bruce.
There was, however, some good news from the Tigers treatment room, with long-term absentees Allan McGregor (ribs/kidney) and Paul McShane (ankle) progressing well as they eye Wembley.
Bruce said: "McGregor has got a hell of a chance the way he's going at the moment.
"McShane is coming along well too and we'll see how they progress in the next couple of weeks."