Police Chief Surachate Hakparn said the 18-year-old woman, Rahaf Mohammed Alqunun, would leave late Friday evening. He gave no other details.
He earlier said several countries including Canada and Australia were in talks with the UN refugee agency on accepting Alqunun.
A spokesman for Canada's foreign minister said he could not confirm she was coming to Canada.
Alqunun's case has highlighted the cause of women's rights in Saudi Arabia. Several female Saudis fleeing abuse by their families have been caught trying to seek asylum abroad in recent years and returned home. Human rights activists say many similar cases have gone unreported.
Alqunun was stopped last Saturday at a Bangkok airport by immigration police who denied her entry and seized her passport.
She barricaded herself in an airport hotel room and launched a social media campaign that drew global attention to her case. It garnered enough public and diplomatic support to convince Thai officials to admit her temporarily under the protection of U.N. officials, who granted her refugee status on Wednesday.
If Canada is taking Alqunun, it could further upset Saudi-Canada relations. In August, Saudi Arabia expelled Canada's ambassador to the kingdom and withdrew its own ambassador after Canada's foreign ministry tweeted support for the arrests of women's right activists. The Saudis also sold Canadian investments and ordered their citizens studying in Canada to leave.
Alqunun had previously said on Twitter that she wished to seek refuge in Australia.
Australian Foreign Minister Marise Payne met with senior Thai officials in Bangkok on Thursday. She later told reporters that Australia was assessing Alqunun's request for resettlement.
Payne said she also raised Australia's concerns with Thai officials about Hakeem al-Araibi, a 25-year-old former member of Bahrain's national soccer team who was granted refugee status in Australia in 2017 after fleeing his homeland, where he said he was persecuted and tortured.
He was arrested while on holiday in Thailand last November due to an Interpol notice in which Bahrain sought his custody after he was sentenced in absentia in 2014 to 10 years in prison for allegedly vandalizing a police station — a charge he denies. Bahrain is seeking his extradition.
Al-Araibi's case is being considered by Thailand's justice system, she said.