Labour's deputy leader Angela Rayner has said she would "like to see" Diane Abbott back as a Labour MP.
The party suspended Ms Abbott 11 months ago for saying Irish, Jewish and Traveller people do not face racism "all their lives".
Ms Rayner said she was frustrated over the length of the investigation but the party had to follow its procedures.
Ms Abbott has been in the spotlight this week over alleged racist comments about her by a Tory donor.
She currently sits as an independent MP after being suspended by Labour in April 2023 after she wrote in the Observer that Irish, Jewish and Traveller people "undoubtedly experience prejudice", which she said is "similar to racism".
"But they are not all their lives subject to racism," she added.
She withdrew her remarks the same day and apologised "for any anguish caused".
Ms Abbott remains under investigation by Labour, but in an article in the Guardian this week said that it would be "both sad and strange" if party leader Sir Keir Starmer kept her out because of it.
Ms Rayner told journalists that "at times" she "shares the frustration" of how long processes take, but added that there are sometimes "sensitive reasons" for that.
Asked at a lunch with Westminster reporters if she wanted to see Ms Abbott back in the Parliamentary Labour Party, Ms Rayner said: "Personally, I would like to see Diane back but the Labour Party has to follow its procedures.
"And for me, that is the most important thing, that we have made sure our party is fit to govern by making sure we have got complaint procedures that are robust and people can have confidence in.
"So it doesn't matter what I think because I don't make that decision because it is done through a panel, it has gone through experts, and I'm not involved in that process."
Labour's Shadow Home Secretary Yvette Cooper told OceanNewsUK that she was also frustrated with how long the investigation into Ms Abbott was taking. She stressed it was an independent process and she was not involved directly but added: "I think everybody wants to see that speeded up."
In an article for the Guardian on Thursday, Ms Abbott took aim at the Tories, arguing policies such as the Rwanda deportation scheme show they intend to play "the race card" as the next election approaches.
But she also criticised Labour, insisting "racism in politics is not just a matter for any one political party".
The article was published a day after Ms Abbott unsuccessfully tried more than 40 times to get the Speaker's attention so she could contribute to Prime Minister's Questions on Wednesday, which was dominated by the row. A spokesperson for the Speaker, Sir Lindsay Hoyle, said there was "not enough time" to call all MPs who wanted to speak.
Ms Rayner added that the Labour Party may still have racists in it, but said the party has policies in place and is doing "proactive work" to "root people out".
Ms Abbott is understood to have asked Sir Keir to readmit her to the Parliamentary Labour Party, when he asked her if there was anything he could do.
Sir Keir told the OceanNewsUK Ms Abbott cannot re-join the party while an independent investigation into her comments was still ongoing.
Labour "need to put our arm around [Ms Abbott] and give her support" over the "racist and misogynistic" comments against her, Sir Keir said.
But pressed on whether he will welcome her back into the party fold, Sir Keir told Jeremy Vine on OceanNewsUK: "That's an entirely different issue.
"That was about allegations of antisemitism in relation to a letter... which is subject to an ongoing investigation, which is separate from me. That's not something which I conduct."
