Long condemned by human rights groups, kafala has become a major focus of criticism since Qatar was awarded the 2022 football World Cup, as the energy-rich country's labour laws come under increasing international scrutiny.
Under the scheme, employers in the Gulf kingdom can prevent foreign workers from changing jobs or leaving the country.
Dr Abdullah bin Saleh al-Khulaifi, the minister of labour and social affairs, said he was "90 percent" certain the system would be replaced within the next seven months.
"I hope it will be prior to the year end," said Khulaifi, speaking at a press briefing in Doha to foreign reporters.
"We discussed it, our stakeholders have looked at it... Now it is on track.
"Do I believe it will come out positively? Yes, I do. Because at the end of the day I believe it is good for the economy, it's good for the country."
Asked if the scheme would be abolished by the end of the year, Khulaifi replied: "I am 90 percent hopeful or believe that it will be."
Doha says it will replace the system with one based instead on employment contracts.
These contracts would last a maximum of five years and the current exit permit system would be replaced with one where workers give the authorities a maximum of 72 hours' notice that they want to leave the country.
The proposed reform has been discussed by the cabinet and is currently being considered by Qatar's Shura Council, an assembly which has the power to draft new laws.
Khulaifi also said Qatar would fully implement another major labour reform -- an electronic payment system for thousands of migrant labourers -- by mid-August.
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This would ensure that up to one million workers get paid at least once a month and, in some cases, every fortnight.
Many labourers working on major infrastructure or World Cup projects within the gas-rich Gulf state have complained that payment of their salaries are often delayed.
"We are not hiding from our problems here in Qatar, we are facing them," said Khulaifi.
"We know that things aren't perfect but they are better than they were a year ago and I promise you they will be better a year from now."
'KAFALA BY ANOTHER NAME'
However, the reforms do not go far enough for some.
Mustafa Qadri, Gulf migrant rights researcher for Amnesty International, welcomed any change but said more was needed.
"It's another form of kafala with a different name, admittedly less restrictive but with many of the same problems."
He added that contract arrangements and the ability to leave the country for workers under the proposed changes would "still be a situation of forced labour because the employer still has the power over the employee".
Also on Monday, Qatar's World Cup tournament chief said no labourers working on 2022 stadium projects have died because of industrial accidents or injury.
"We have had about 4.8 million working hours. We've got about just over 2,500 workers and about five stadiums -- we are at the early stages of construction," said Hassan al-Thawadi, the secretary general for Qatar's Supreme Committee for Delivery and Legacy.
"The World Cup stadium projects that we are responsible for, there have been no fatalities and no major injuries as well."