Braverman was caught speeding last year and sent a letter giving her the option of paying a fine and accepting three points on her licence, or attending a speed awareness course - as is often the case for minor speeding offences.
A spokesman for Sunak said on Monday the Prime Minister "wants to avail himself of all the information before he makes a decision".
He added: "He has spoken to the Home Secretary about this, but I’m not going to get into the detail of that conversation. I’m not going to pre-empt that and set out his view before he’s done that.”
The issue arose when Braverman reportedly asked civil servants to arrange a private course for her - but she was told it was not part of the civil service remit. She later reportedly asked a special adviser to arrange a course for just her, but opted to pay the fine and accept the points when she was told there was no option to do this.
On Monday, Braverman indicated she had no intention of stepping down from her position, insisting there was “nothing untoward” about her handling of the offence.
Now, critics are calling for her to face an investigation over whether her actions were a breach of ministerial code, which states that ministers must uphold impartiality of civil servants.
What happens when ministers break the ministerial code?
Braverman appeared to have suffered a "real lapse of judgement" a former senior civil servant told BBC Radio 4.
"Obviously, there's still investigations to be done and so on but the code is very clear. Ministers must ensure that no conflict arises or appears to arise between their public duties and their private interests," Sir Philip Rycroft said.
"Even asking a question of a civil servant as to how she might go on one of these courses puts them in an impossible position."
According to the ministerial code: "Ministers must uphold the political impartiality of the Civil Service, and not ask civil servants to act in any way which would conflict with the Civil Service Code and the requirements of the Constitutional Reform and Governance Act 2010."
Labour leader Sir Keir Starmer told BBC Breakfast that it appeared "inappropriate action took place" from Braverman that "needs to be fully investigated".
"The usual consequence of breaking the ministerial code is that you'll go," he said.
If Braverman is found to have breached the ministerial code, she could be forced to resign or stand down - however, new rules introduced by former prime minister Boris Johnson mean this sanction is not automatic.
According to the ministerial code, the prime minister could ask the cabinet office to investigate or refer the case to the independent adviser on ministers’ interests. However, the prime minister would make the ultimate call on sanctions, if any were suggested.
It is understood Braverman was in Downing Street on Monday for a regular meeting on illegal immigration, but no details of her meeting with the PM have been released by Number 10.
What happens next?
Sunak is thought to be consulting an ethics adviser over the claims, but did not comment on whether he would be launching an investigation into Braverman.
"I don't know the full details of what has happened, nor have I spoken to the home secretary," Sunak said from the G7 summit.
"But I understand she has expressed regret for speeding, accepted the penalty and paid the fine."
A source from Downing Street told The Independent: “The prime minister has always followed the proper process in these matters, and will consult the independent adviser upon his return to London."
The home secretary is scheduled to face MPs at Home Office questions on Monday.