Pressure is building on Labor senator Sam Dastyari to quit the Parliament, including from within the ALP.

Key points: Fairfax report alleges Sam Dastyari urged Tanya Plibersek not to meet with pro-democracy activists in Hong Kong

Fairfax report alleges Sam Dastyari urged Tanya Plibersek not to meet with pro-democracy activists in Hong Kong Catherine King and Linda Burney both say the embattled senator should "consider his future"

Catherine King and Linda Burney both say the embattled senator should "consider his future" Coalition figures renewing demands for Bill Shorten to tell Senator Dasytari to quit

Senator Dastyari is again being pressured to go because of a report in Fairfax Media that he urged Labor's deputy Tanya Plibersek not to meet pro-democracy activists in Hong Kong.

Fairfax said it had confirmed this with multiple sources who say the intervention by one of her colleagues surprised Ms Plibersek.

Rumours of attempts by Senator Dastyari to lobby Ms Plibersek over her visit to Hong Kong have circulated in Canberra for more than a year.

He has since denied that report, saying it did not occur, but Ms Plibersek's spokesman told the ABC the meeting with the activist in Hong Kong went ahead as scheduled.

Labor's health spokeswoman Catherine King said Senator Dastyari should reflect on his future.

"We have been very, very clear about the matter of Sam Dastyari, that his political career is, in essence, going nowhere," she said, referring to Labor leader Bill Shorten twice dumping the Senator from senior jobs.

"Bill has been very clear about that and has said that he has paid a price for his actions.

"And I think that those are all matters for Sam to reflect on."

Ms King was echoing the words used last Friday by Mr Shorten when he said Senator Dastyari's career was "going nowhere fast".

When asked if she was comfortable with Senator Dastyari continuing to sit in the Senate, Ms King said it was "a matter for Sam".

She described the senator as someone who has been a very effective politician.

"But I think that Bill has made it very, very clear that Sam’s political career is not going very far and I think they are matters for Sam to reflect upon," she said.

Labor frontbencher Linda Burney also said this morning "it is now up to Mr Dastyari to consider his position".

"And I am sure he is doing that," Ms Burney told Sky News.

"In relation to the continued role of Sam within the Parliament, that is a matter I think very much for Sam.

"Sam Dastyari, I am sure, is thinking very deeply about his role within the party."

Dastyari a 'double agent', Dutton says

Coalition figures have renewed their demands for Mr Shorten to tell Senator Dasytari to quit.

Immigration Minister Peter Dutton called Senator Dastyari a "double agent" and said he must resign from the Senate.

Senior Labor frontbencher Tony Burke dismissed that as "the most pathetic overreach imaginable".

"Peter Dutton is good at overreach, he does it a lot, he went to a new level of spectacular today in ridiculous overreach," Mr Burke said on Monday.

"There is no argument, there is no allegation that would substantiate what Peter Dutton is claiming there."

Environment Minister Josh Frydenberg told RN: "The Dastyari itch is soon becoming a rash and will be an outbreak engulfing the whole of the Labor Party unless Bill Shorten shows Sam Dastyari the back door."