A YouGov survey of more than 17,000 fans from 15 countries - 10 of them European - commissioned by Amnesty showed that 73% of respondents would support the proposal and 10% opposed it.
More than two-thirds of respondents (67%) also said their national Football Associations should speak out publicly about the human rights issues surrounding the World Cup in Qatar as well as call for compensation for migrant workers.
"Across the globe, people are united in their desire to see FIFA step up and make amends for the suffering endured by migrant workers in Qatar," said Steve Cockburn, Amnesty International's Head of Economic and Social Justice.
"The past cannot be undone, but a compensation programme is a clear and simple way that FIFA and Qatar can provide at least some measure of redress to the hundreds of thousands of workers who made this tournament possible."
FIFA said a wide range of measures had been implemented in recent years to improve protection for workers in Qatar.
"FIFA takes note of the poll conducted on behalf of Amnesty International, featuring respondents from 10 countries in Europe and five countries from the rest of the world," the governing body said in a statement.
"Respondents may not be fully aware of the measures implemented in recent years by FIFA and its partners in Qatar to protect workers involved in the delivery of the FIFA World Cup Qatar 2022."
In May, Amnesty and other rights groups called on FIFA to set aside $440million to compensate migrant workers in Qatar for human rights abuses.
FIFA had said in May it was assessing Amnesty's proposition and had already compensated a number of workers, who had received $22.6million as of December, 2021.
The government of Qatar has said that its labour system is still a work in progress, but denied a 2021 Amnesty report that thousands of migrant workers were still being exploited.
Amnesty also called on FIFA and Qatar to establish a remediation programme to reimburse unpaid wages, recruitment fees paid by hundreds of thousands of workers and compensation for injuries and deaths.
"The programme should be established, and an initial meeting held between key stakeholders, before the tournament kicks off on 20 November 2022," Amnesty said, adding that workers and trade unions should be involved in the programme.
"The programme should also support initiatives to protect workers' rights in the future."
