The news outlet said representatives of the government and Germany's flagship carrier had agreed on those key points on Monday but Lufthansa Chief Executive Carsten Spohr had not officially taken part in the discussions.
It said Spohr wanted to formally seal the deal with Chancellor Angela Merkel and Finance Minister Olaf Scholz on Tuesday.
Business Insider cited negotiating sources as saying it was unlikely the package would be re-opened at this stage.
Lufthansa declined to comment on the report. The German government had no immediate comment.