The suspension was due to a shortage of capital, but the company has approached three groups of investors, FAT Chairman Chang Kang-wei said at a press conference Friday.
Chang said if the funds are secured, he hopes flights could be resumed as early as Friday afternoon.
The sudden decision to suspend operations had triggered outcries from passengers and serious warnings from the authorities.
The island's aviation authority warned Thursday that the airline may face a fine of up to 3 million new Taiwan dollars (about 98,500 U.S. dollars) and have its license withdrawn.
As of Friday afternoon, the island's aviation authority has not announced its decision on whether to allow FAT to resume operation.
Established in 1957, FAT declared bankruptcy in 2008 but resumed operation three years later after restructuring.
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