Labor's plan to put Aboriginal elder Pat Dodson into the Senate is in limbo, with the man he is set to replace, Joe Bullock, yet to officially resign from the Upper House.

The issue is causing concern in Labor ranks with a critical debate over the Government's building and construction bill just a fortnight away.

After less than two years in the Senate, Joe Bullock dumbfounded colleagues when he announced he was quitting because of Labor's support for same-sex marriage.

"If your job requires you to do something you believe to be wrong, there's only one course of action open, resign," he said at the time.

That was five weeks ago, but Senator Bullock is yet to tender his official resignation with the president of the Senate.

Pat Dodson was handpicked by Opposition Leader Bill Shorten to replace Senator Bullock.

Mr Dodson said no-one had told him when he would take his seat.

"I understand he's [Senator Bullock] grappling with that and really it's a matter for the state Labor of Western Australia and others to sort through," Mr Dodson said.

"I expect when people say they're going to do something, it's going to be done."

Labor Party unable to confirm resignation date

Neither the WA Labor Party nor Mr Shorten's office was able to confirm when Senator Bullock was resigning.

However a spokeswoman for Mr Shorten said the issues were being addressed.

"The party is working through these matters. Mr Dodson will take his position upon conclusion of the proper processes," she said.

But the delay is causing concern in Labor ranks, with both houses of Parliament being recalled on April 18 to deal with the Federal Government's building and construction bill.

It is not known if Senator Bullock planned to return to Canberra for the vote.

If he does not, there is concern there will not be time for Mr Dodson to take his place.

When Senator Bullock does tender his resignation, a joint sitting of State Parliament will need to be scheduled to sign-off on his replacement.

The WA Parliament is sitting this week, before taking a four-week break.

While campaigning in Perth, Mr Shorten sent a message to local powerbrokers that he would intervene if necessary to make sure Mr Dodson was given a winnable seat in the event of an early election.

"I think my track record in terms of supporting Pat Dodson is superior to anyone else," Mr Shorten said.

Senator Bullock did not return the ABC's calls.