Ex-minister Lord Falconer has met Labour’s general secretary Jennie Formby to discuss a role investigating anti-Semitism in the party.
The peer suggested on Sunday he could review Labour’s internal complaints process, strongly criticised by MPs who have recently quit the party.
But the BBC’s Iain Watson said he had yet to agree to take the role pending more talks on the resources available.
Senior figures in the party have clashed over the issue in recent days.
Mrs Formby has accused deputy leader Tom Watson of “undermining” her by seeking to get involved in complaints.
She said his call for all complaints about anti-Semitism to be forwarded to him for monitoring was “completely unacceptable”.
The party has been plagued by accusations of anti-Semitism since mid-2016.
The leadership has been accused of tolerating a culture of anti-Semitism by a number of MPs who have quit the party, including Luciana Berger and Joan Ryan.
Last week, the Labour MP Chris Williamson was suspended after saying the party had been “too apologetic” and “given too much ground” to its critics.
According to newspaper reports over the weekend, Lord Falconer was to be asked to audit the party’s complaints and decision-making process in the new role of surveillance commissioner.
The former justice secretary told the Sunday Times he expected to undertake a review lasting “months not years”.
The Labour peer said he wanted to restore faith in the party’s disciplinary procedures, saying many Labour members believed the outcome of cases depended on “who your friends are”.
The BBC understands that talks are continuing about the role.
Labour said Monday’s meeting was “nothing out of the ordinary” as the two “meet all the time”.
Over the weekend, shadow chancellor John McDonnell backed Mrs Formby in her row with Mr Watson, after the deputy leader claimed there had been a “loss of trust” in the party’s processes.
Mr McDonnell, a close ally of Jeremy Corbyn, said it “wouldn’t be right” for Mr Watson to get involved in individual cases as they had to be dealt with by the party itself.