The UK's Financial Conduct Authority has faced criticism for its role in overseeing the sale of British mutual insurer LV (formerly Liverpool Victoria) to Bain Capital.
In a letter seen by the Daily Mail, the chairman of the All Party Parliamentary Group for Mutuals Gareth Thomas asked the FCA to expose details of the negotiations, including whether LV had been offered more money by mutual insurer Royal London.
While Royal London cannot legally confirm if its offer was higher, it has been reported that it offered £540m to Bain's £530m.
The move first came under fire earlier this year, but as the voting deadline of 10 December approaches, pressure has intensified. The FCA said last month that it had "no objections" to the take-over, and it would continue to scrutinise the situation closely.
If the sale to Bain is approved, ordinary members would each be given £100 and with-profits members would receive an additional boost when their policies mature.
The Daily Mail said that the letter read: "It is now clear that the two most valuable bids received by the Liverpool Victoria board were from Bain Capital and crucially, another mutual, Royal London.
"Will you confirm what many have explicitly suggested; that Royal London offered more money than Bain Capital?"
It added that the over one million members who own LV cannot make a "complete assessment" of the bids without receiving the full details.
The Daily Mail also said that the letter urged the FCA to release any information it has about how much chief executive Mark Hartigan and chairman Alan Cook will be paid if the deal passes.
While Hartigan claimed he will receive nothing, it has been reported that he will receive a stake in the company and a pay rise if the takeover goes ahead, with Cook keeping his job, after both expecting to lose their jobs under a takeover by Royal London