The seven-member coalition has also demanded that Qatar close a Turkish base and downgrade its relations with Iran. The deadline, which had been extended, expired Wednesday, according to The Associated Press.
"Asking him to close a base where Turkish troops are stationed, downgrade relations with Iran and close Al-Jazeera, the flagship satellite channel in the Middle East, would be humiliating," Kattouf said on "Squawk Box."
"So there's no way out of this immediately."
The coalition, which includes Egypt, Bahrain and the oil-rich United Arab Emirates, cut diplomatic ties with Qatar three weeks ago, accusing it of supporting terrorism.
"They're like kids in a tough neighborhood who have too much lunch change in their pocket," said Kattouf, president of Amideast, which works to foster Americans' understanding of the Middle East.