The due diligence will take some additional weeks, a source close to Hapag Lloyd's owners said, adding that bids from Oman's Onyx Investments and China's fourth-largest airline group HNA were expected by end of July.
TUI said in April that it expected the sale to take place by the end of May.
TUI currently owns 49 percent of Hapag-Lloyd, but that stake is due to shrink to about 38 percent in late May as it has agreed to sell about 11 percent of shares to co-owner Albert Ballin, a consortium of investors.
Another source quoted by Reuters who is close to Hapag's owners confirmed the delay, saying, "I do not expect a decision before the summer break."
"The interest of the bidders is strong, talks are taking place on an almost daily basis," the first source said, adding price indications were strong enough to keep the process alive.
TUI, Hapag-Lloyd and the bidders declined to comment.
Onyx and HNA were not immediately available for comment.