There are concerns the looming local elections will be overshadowed by questions surrounding the Labour deputy leader's house sale in 2015.
A Labour figure is pushing for Ms Rayner - who denies any wrongdoing to disclose the financial advice she was given and ask HM Revenue and Customs to get involved.
They said: "If Keir wants a missionled Government, then that mission should be to clean up politics, and this needs to begin with the transparency of Angela's tax affairs."
Tensions came to a head last week when Greater Manchester Police said it was reassessing its decision not to investigate whether she gave false information on official documents.
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