The accountancy watchdog, which conducted a five-year investigation, suggested the fine in a public hearing on Thursday after the Big Four firm admitted to failings in the 2009 audit, the Financial Times reported.
The retired partner Stephen Harrison, who oversaw the audit, was also asked by the FRC to pay a fine of £200,000.
PwC admitted failure to exercise appropriate scepticism or gather sufficient evidence while auditing Connaught, but argued that they had been misled by the company’s management.
As a result, PwC’s defence lawyer Tom Adam suggested a fine of £2m to £2.5m to the firm and £50,000 to Harrison.
The tribunal members have not yet approved the sanction, according to FT.
An FRC spokesperson said the chair of the tribunal would be publishing his report “in due course”.
The former FTSE 250 social housing maintenance firm collapsed in 2010, saddling creditors with major losses and costing hundreds of jobs.
The accounting regulator alleged that Harrison and PwC “failed to act with competence and due care” in relation to the audit of the financial statements for the group, Connaught Partnership Limited and Connaught Compliance Limited.
It also claimed that their conduct fell significantly short of the standards reasonably to be expected of a member or member firm of ICAEW.
Last month, the FRC launched an investigation into PwC's audit of the IT services provider Redcentric. Following the conclusion of an independent probe into Redcentric’s accounting practices, the company was forced to restate its consolidated financial statements and other financial information relating to those years.
As a result, the FRC said it would consider issues regarding misstated accounting balances during its inquiry.