Germany's second-largest airline, Air Berlin, was forced to cancel dozens of flights on Tuesday due to an unusually high number of pilots calling in sick, the company said.
"A stable operation is an essential precondition for successful negotiations", Mr Winkelmann said.
But he added that the firm could if necessary buy up all of Air Berlin's assets, including 140 leased aircraft and prized landing and takeoff slots at German airports.
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TUIfly was also forced to cancel flights a year ago after many pilots called in sick, with their union saying staff were concerned that merger talks, since failed, could lead to job and pay cuts.
"We worked hard to be able to make this offer, with help not only from experts but also supportive comments and suggestions from employees, passengers and business partners of Air Berlin", the Bavarian airline tycoon wrote in a Facebook post late Sunday.
Air Berlin announced on Monday that it would end its flights to the Caribbean from Düsseldorf beginning September 24.
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However, the pilots' union, Vereinigung Cockpit, denied the report, saying: "At no point did the VC call for (pilots) to report ill". At least 32 were canceled Wednesday, though Air Berlin said more pilots were returning. The allowance may reportedly keep the carrier afloat until mid-November with its German jobs put at risk.
Air Berlin made a loss of €782m (£703m) in 2016.
Flights from Air Berlin's key hubs in Berlin and Dusseldorf were especially badly hit by cancellations, the airline said.
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Ryanair said on Tuesday that Air Berlin could be of interest to the Irish low-priced carrier but it didn't want to wait until after Lufthansa had finished talks.