"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."
There is no official figure given for how many illegal residents live in Qatar and the issue is highly sensitive in a country regularly criticised for the treatment of its almost two million-strong foreign workforce, ever since winning the right to host the 2022 football World Cup.
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.
Workers become "illegal" after quitting their job or fleeing 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".