Sarwar told MSPs the alleged comment was “shameful, utterly shameful”.
He added: “And it should shame every member of the SNP government.
“Bribes rather than truth and justice.
“The pain this government has inflicted on these families is through the roof.”
First Minister John Swinney said he was “horrified” by the suffering of bereaved families.
He said the public inquiry had been set up to “give the truth” to the families.
Swinney said he was “appalled” by Sarwar’s calls for inquiry chairman Lord Brodie to consider the role of the Scottish government in construction and opening of the QEUH.
He accused the Labour leader of political interference and said he should be “ashamed” of his conduct.
Scottish Conservative health spokesman Sandesh Gulhane described Prof McQueen’s reported comments as “absolutely disgusting”.
He added: “Grieving families will be furious that someone in such a senior position even thought of saying something so callous and offensive.”
Prof McQueen has been approached for comment.