The working relationship between Julie Bishop and Peta Credlin has reportedly broken down, setting the scene for a potential showdown between the two most powerful women in the country.

News Corp is reporting growing tensions between the Foreign Minister and Prime Minister Tony Abbott's polarising chief-of-staff. It follows a week of damaging revelations about Ms Bishop's apparent frustration with the conduct and influence of Mr Abbott's office.

Foreign Minister Julie Bishop speaks with Prime Minister Tony Abbott's chief-of-staff Peta Credlin. Credit:Alex Ellinghausen

"They are like two Siamese fighting fish stuck in the same tank," an unidentified Coalition frontbencher told The Australian newspaper.