The two shareholders welcomed initiatives launched by Hapag-Lloyd to secure its future and agreed on a further course of action for the company.
A source close to the deal said a more detailed agreement should be reached by the end of July and that the exact amount of financing needed was still unclear.
"One line of reasoning says Hapag-Lloyd will get around 1.75 billion euros ($2.44 billion)," said this person, who is close to the proceedings. Around a 1 billion of this could come from state-backed loans through banks and 750 million euros would then have to be supplied by the company's investors, the person said.
Both TUI and Ballin denied to comment on the amount of an investment that Hapag-Lloyd might need.
The Albert Ballin consortium -- which includes the state of Hamburg, regional lender HSH Nordbank , logistics entrepreneur Klaus-Michael Kuehne and two insurance groups -- owns a 57 percent stake in Hapag, while 43 percent is held by former parent TUI.
TUI agreed in October to sell Hapag-Lloyd to the investor group for an enterprise value of 4.45 billion euros ($6.07 billion), but the financial crisis threw a spanner in the works.
TUI ended up keeping a larger than initially planned stake and also agreed to provide additional credit facilities of up to 1.1 billion euros for a limited time to secure the unit's financial stability.