Fatima Payman enlists minor party specialist as Labor braces for ...

Suspended Labor MP Fatima Payman has enlisted the advice of a minor party political "whisperer" as her party colleagues brace themselves for the possibility she will move to the cross bench.

Prime Minister Anthony Albanese handed Senator Payman an indefinite suspension on Sunday after she said she would continue to defy the party's position on Palestinian recognition in parliamentary votes.

On Monday, the West Australian senator said she had been "exiled" by her colleagues and would reflect on "the best way to represent the people of Western Australia," opening the door to a party exit.

Prime Minister Anthony Albanese told 7.30 he was not sure if Senator Payman would still be with the Labor Party by the end of the week.

"That is a decision for her," Mr Albanese said.

"She has made a decision that she can't be bound by what puts our team together.

"I would like to see her rejoin the team and that option is certainly available to her."

Glenn Druery, a political operative nicknamed "the preference whisperer" for his history of helping minor parties achieve political success, told the ABC he had had "informal conversations in recent days with Senator Payman."

Mr Druery also said he had had "informal conversations with the Muslim community" about election strategies.

Asked if he was bothered by Senator Payman having conversations with people who want to thwart the government agenda, the prime minister said her moves were not his primary concern.

"I'm not focused on it, I've got a big job," he told 7.30.

It comes as a Western Sydney-based group called The Muslim Vote plans a "teal-style" political campaign to unseat Labor MPs by mobilising Muslim community anger over the government's stance on Gaza and on the question of Palestinian recognition.

A spokesperson for the group told the ABC it was a "grassroots" movement with over 2,000 volunteers and was preparing to endorse candidates in the Labor-held seats of Blaxland, Watson, McMahon and Werriwa.

"It is the first time that the Muslim community has realised that their vote does matter," the spokesperson said. "This has been a line in the sand."

Education Minister Jason Clare's seat of Blaxland is among those The Muslim Vote plans to target at the next federal election.(ABC News: James Carmody)

Mr Druery did not specify which Muslim community group had contacted him and added he was not paid for his advice to the community group or Senator Payman.

"I believe in multi-party democracy and diversity in politics," he said.

But senior Labor sources believe the two are linked and that Senator Payman is actively considering aligning with The Muslim Vote. The group's spokesperson said "no formal discussions" had been had to that effect but that he could not rule it out in future.

The federal Labor caucus unanimously endorsed the PM's decision to suspend Senator Payman at a meeting in Canberra on Tuesday, and senior Labor MPs have privately expressed their frustration at her conduct.

But outside the parliament, Labor party members have voiced anger at the senator's treatment.

NSW Labor MP Anthony D'Adam, the co-convenor of Labor Friends of Palestine, told the ABC "the vast majority of the party membership think that the position she's taken is the right one on the right side of history, and want Labor to be on the right side of history."

Mr D'Adam said local Labor branches were passing resolutions "calling on the party to make a much stronger position."

"I think most ALP members look at the situation in Gaza and are horrified and expect Labor would be more strident in its criticisms of Israel," he said.

Mr Albanese remained staunch on the government policy though.

"We have consistently supported a two-state solution,” he told 7.30.

“The problem with the motion that was moved by the Greens is it forgot to mention Israel. 

“A one-state solution, whether it is Israel or Palestine is not in the interests of Israelis or Palestinians."

Senator Payman said on Sunday she had received a strong supportive response from Labor party members, and her social media pages have hundreds of supportive comments including from many people who identify themselves as party members.

Kos Samaras, director at polling group RedBridge, said he believed Labor had handled the matter poorly and might experience an electoral fallout.

"The top three electorates with the highest numbers of Australian Muslims in them are Blaxland, Watson and Calwell," he told the ABC.

"In Calwell [in Melbourne's northwest] more than 20 per cent of the electorate is of Islamic faith. But the question is how much of them do you see in Labor's primary vote?

"If you look into it, it's close to half. So if this issue switches votes, much of your primary vote goes out the window. I don't think they comprehend how serious of a problem this is."

Mr Samaras said The Muslim Vote appeared to be planning a "well-financed and well-structured" and had a reasonable chance of success.

"If they pull this off and are able to run a high-profile prominent independent who is well-known locally, you can see a situation where the primary vote plunges and Labor is in real trouble, especially if the Liberals preference the independent."

Mr Samaras pointed to the example of Fowler, where well-known local Dai Le won a previously safe Labor seat by capitalising on community anger about "parachuted" Labor candidate Kristina Keneally.

"The other dynamic which happened in Fowler is the Liberals realised there was a better chance to remove the Labor MP by tactically voting.

"Labor is already under pressure in these outer suburban electorates because of cost of living, now that's compounded with a problem in diverse electorates. I don't see why they didn't give their MPs a conscience vote."