The two players clashed at Oakwell back in November 2008 when Morgan's elbow left Hume with a fractured skull and internal bleeding, which forced the Canada international to miss the second half of last season.
Hume was stretchered off and later spent 48 hours in the high dependency unit at Salford Royal Hospital following emergency surgery. He was readmitted to hospital a fortnight later due to complications.
Morgan, who has always maintained his innocence, claimed his elbow accidentally caught Hume on the side of his head. He received only a booking from referee Andy D'Urso and the Football Association later decided to take no further action.
Hume, who made his comeback for Barnsley in August, is still considering legal action against Morgan and said last month if he would shake hands: "I really don't know. It's one of those isn't it? The professional thing would be to say yes. I probably would - but it would be the quickest handshake in the world."