A new report has claimed 185 Nepalese workers died last year including on projects on the infrastructure for the tournament.
FIFA secretary general Jerome Valcke has written to the organising committee - now known as the Supreme Committee for Delivery and Legacy in Qatar - demanding answers ahead of a hearing in the European Parliament the following day.
FIFA's German member Theo Zwanziger, who has been given the responsibility of dealing with the issue for the world governing body, said: "We are currently in the middle of an intensive process, which is exclusively aimed at improving the situation of workers in Qatar.
"Ultimately, what we need are clear rules and steps that will build trust and ensure that the situation, which is unacceptable at the moment, improves in a sustainable manner.
"This process will continue after February 13 and will culminate in a report to be delivered to the FIFA executive committee at its meeting on March 20 and 21."
FIFA president Sepp Blatter visited Qatar after concerns were raised by an investigation carried out by The Guardian last year, but the latest figure of deaths was revealed by the Pravasi Nepali Co-ordination Committee (PNCC) last week.
A FIFA statement said: "The Supreme Committee for Delivery and Legacy in Qatar shall provide FIFA by February 12, 2014 with a detailed report on the improvement of working conditions in Qatar.
"This was communicated today by FIFA in a letter from secretary general Jerome Valcke to the competent body in Qatar.
"The report will then be used to prepare for the hearing at the European Parliament in Brussels on February 13, 2014, which will be attended by Dr Theo Zwanziger as the FIFA representative mandated to deal with this matter.
"FIFA expects to receive information on the specific steps that Qatar has taken since FIFA president Blatter's last trip to Doha in November 2013 to improve the welfare and living conditions of migrant workers."
FIFA said it would continue talks on labour rights in Qatar with different stakeholders, and define the exact responsibilities of the various parties involved - FIFA itself, the state of Qatar, companies operating in the country plus international labour organisations.
Zwanziger has met representatives from human rights and labour organisations in recent weeks, including Amnesty International.