As a procession of business vendors severed ties with the two-year-old site following the storming of the U.S. Capitol last week, Matze said in an interview with Reuters on Wednesday that he does not know when or if it will return.
"It could be never," he said. "We don't know yet."
The app said in a legal filing it has over 12 million users.
Matze said that Parler was talking to more than one cloud computing service but refused to disclose names, citing the likelihood of harassment for the companies involved. He said the best thing would be if Parler could get back on Amazon.
Parler on Monday filed a lawsuit against the company, which Amazon said has no merit. Matze said the company was considering suing other vendors but declined to say more.
Amazon cut Parler, a platform favored by supporters of U.S. President Donald Trump, off its servers this weekend for failing to effectively moderate violent content. Apple and Alphabet's Google also kicked Parler from their app stores.
"It's hard to keep track of how many people are telling us that we can no longer do business with them," said Matze.
Amazon on Tuesday filed exhibits that showed it had warned Parler late last year about vile and threatening language on its site before cutting off the platform after the attack on the U.S. Capitol.
Matze said Parler had also been booted from online payments service Stripe and from American Express and had lost its Scylla Enterprise database.
Parler could not send SMS messages after being banned by Twilio and could not use Slack to contact its "jury" of paid and volunteer users who make Parler content moderation decisions after being ditched by the workplace messaging app.
The vendors did not immediately respond to Reuters' requests to comment.