Last week authorities in the Gulf State admitted that staff were being badly treated and promised to reform labour laws.
But campaigners say concerns remain following a lack of detailed pledges that matters will improve.
Mr Murphy will tell the Prospect Conference in Glasgow, including members of the Scottish Senior Football Referees Association, that the SFA should "stand" with football fans who do not want a major sporting event delivered on the back of workers' suffering.
"Everyone in the world seems to have a view on the Qatar 2022 World Cup except the SFA," he will say.
"Even the Qatari authorities now admit that migrant workers are being exploited - yet the SFA has refused to break its silence."
He will add: "Football fans around the world want action to ensure that the Qatar 2022 World Cup is not delivered on the back . It is time the Scottish FA stood with them."
Mr Murphy, Labour's shadow international development secretary, has been leading a campaign on the issue.
He visited the Qatari capital, Doha, earlier this year to meet officials and observe the treatment of migrant workers.
Amnesty International and Human Rights Watch, among others, have warned of widespread abuse.
It is understood that the SFA had discussions with Scottish Sports Minister Shona Robison before she wrote a letter setting out her serious concerns about the potential abuse of workers in Qatar.