The Slovenia international was forced out of Tuesday night's defeat at Wolves with a calf injury and is a major doubt.
Striker Jay Simpson replaced Koren in midweek, but midfielder Tom Cairney provides manager Steve Bruce with an alternative option.
Midfielder Corry Evans sits out the second of his two-match ban after reaching 10 yellow cards.
But the Tigers were boosted by the surprise return to the substitutes' bench of defender Paul McShane at Molineux and he hopes to feature.
The Irishman had been expected to be out for the rest of the season when damaging ankle ligaments last month.
Matty Fryatt is hoping to play an extended role. The striker returned to the bench at Ipswich last weekend following a season-long Achilles injury and made his second league appearance of the season on Tuesday.
Hull can seal automatic promotion with victory if Watford fail to beat Blackburn on Saturday.