German media reports last month said the United Arab Emirates-based airline could increase its stake in the struggling German carrier to 49.9 percent from the current 30 percent.
Etihad has also been studying a possible investment in Italian carrier Alitalia in recent months, but the CEO said on Monday that this process was still ongoing.
"We are in due diligence at the moment. The mandate we have from shareholders is if we can achieve an agreement that meets the commercial mandate, we'll come back and present that to the board. That's where we are at the moment," Hogan said.