Midfielder Cook strained ankle ligaments during England Under-19s' win against Azerbaijan last Saturday and will also be doubtful for Monday's clash at Wolves.
Rudy Austin could return to the starting line-up in Cook's absence following a thigh injury, while January loan signing Granddi Ngoyi is also hoping to feature.
Head Coach Neil Redfearn has no other injury problems as Leeds bid to extend their unbeaten run to six matches.
Blackburn could hand a debut to Paul Taylor following his arrival on loan.
Rovers acquired the Ipswich winger on the day the loan window closed and he could play his first Sky Bet Championship game since December.
Gary Bowyer could be forgiven for having half an eye on Wednesday's FA Cup quarter-final replay with Liverpool when choosing his team, with Taylor and Jay Spearing both ineligible to face Brendan Rodgers' men while goalkeeper Simon Eastwood tends to be preferred to Jason Steele in cup competitions.
Bowyer kept his cards close to his chest in terms of his injured players but Marcus Olsson (hamstring), Josh King (hamstring), David Dunn (calf) and Grant Hanley (calf) are due to return soon, although Jason Lowe (foot) and Shane Duffy (knee) will not play again this term.