Sky News reports the transatlantic carrier made a preliminary offer for the division earlier this week.
It follows speculation Lufthansa was looking at Condor, Cook’s German short-haul carrier.
Boss Carsten Spohr said its bid could eventually extend to the rest of Cook’s airline division, including its UK operation.
Wizz Air’s private equity backer Indigo Partners is also understood to be interested in Cook’s airline business, which was placed up for sale in February.
