The England international picked up a minor hamstring injury in Belarus last week and the Anfield boss has confirmed that the midfielder will not be fit enough to play in the return leg.
However, Rodgers insists the injury is not serious and expects to see Cole back fit and ready to play in a couple of days.
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"It wasn't serious, just a little nick on his hamstring but apart from that everyone else is fit and some players have got some game time and some extra work in.
"Their condition is better, even though it's only a week on from the last game against Gomel, and that will stand them in good stead."