The amnesty runs until December 1 and allows those without the correct paperwork to live and work in Qatar to leave without "legal consequences".
"I estimate that by the end of the amnesty, the number will reach 9,000," said Brigadier Abdullah Jaber Al-Labda, in charge of the Ministry of Interior's Search and Follow Up Department, which is processing the claims of those trying to leave.
"When we first started the numbers weren't high but we are coming to the end of the amnesty and it will speed up," the official told AFP.
The amnesty applies to those in violation of "Law No 4 of 2009", which governs "the entry, exit, residence and sponsorship of expatriates".
Qatari law states it is illegal for foreigners to work in the gas-rich Gulf emirate without a visa.
And, under the current controversial "kafala" sponsorship laws, anyone wishing to change their job must get permission from their employer.
Human rights groups have claimed that many abscond because they have not been paid or have suffered abuse.
Labda says there is "more than one reason" why people flee, but after they do many "are scared to go to the authorities".
Once a worker has fled they can be classified as a "runaway" and exist largely outside the law.
They will have lost their source of income, cannot legally get a new job and in the case of someone working as a domestic maid, lost their accommodation as well.
Any boss caught hiring an illegal worker faces a fine or prison.
Despite this, some manage to evade the law for a long time - one Indian family which left during the amnesty survived without documentation for 16 years, an official at the Search and Follow Up Department said.
Most of those expected to leave during the amnesty come from Asia, say officials, including Bangladesh, India and Nepal.
Qatar has held three such previous amnesties, the last in 2004.
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