The next-generation device was officially unveiled in February with a stated release date of early May, however issues with the phone's folding mechanism forced the South Korean firm to postpone the launch.
A company official told The Korea Herald that no progress had been made with regards to the Galaxy Fold's release date.
"If we are running such a media event this month, we should be doing something by now," the official said.
"Nothing has progressed since the April delay."
The Galaxy Fold, which costs nearly $2,000 (£1,540), was originally hailed by Samsung as the future of smartphones, who claimed it would "overturn expectations and set this industry on a new path".
But within days of review samples being sent out to journalists, reports began to emerge of problems with the folding screen.
Despite Samsung claiming the Galaxy Fold could withstand 200,000 folds without breaking, several reviewers said the foldable phone had become "unusable" after just two days of use.
Samsung CEO DJ Koh told the publication in May that the company was on the verge of revealing a rescheduled release date for the phone, while a different Korea media outlet reported that he had said the Galaxy Fold would arrive before July.
"[Samsung] has reviewed the defect caused from substances [that entered the device] and we will reach a conclusion in a couple of days," Mr Koh said. "We will not be too late."
Samsung did not immediately respond to a request from The Independent for comment on the release date of the Galaxy Fold.
Other smartphone manufacturers have also experienced issues with their plans to launch a folding phone, with Huawei reportedly delaying its Mate X until September.