A government spokesperson said the negotiations were at an advanced stage, but had not been completed.
The online trading platform Tradegate showed Lufthansa shares 4.5 per cent up shortly after German news magazine Der Spiegel reported that the bailout package had been agreed.
Lufthansa is facing the biggest financial crisis in its history due to the coronavirus pandemic, which has grounded around 90 per cent of its planes. It is currently losing about 800 million euros per month.
Many at Lufthansa had resisted suggestions that the German state should take a stake in the firm, with some pushing for a more limited government role.
In a letter to employees, Lufthansa chief executive Carsten Spohr said that a deal was close to being reached.
"Since our liquidity will continue to decrease in the foreseeable future, we hope that political decision-making will be concluded quickly and that a future-oriented compromise will be reached in Berlin that also takes into account our competitiveness in the future," the letter read.
