Federal Labor is seriously considering a royal commission into the banking sector, with the proposal to be formally considered by the shadow cabinet in the coming days.

Opposition Leader Bill Shorten lashed the federal government for inaction over scandals at the major banks on Thursday, while a second Coalition MP, Warren Entsch, called for such an inquiry into the "immoral conduct" of the major banks.

Speculation rippled through Canberra that Mr Shorten had been poised to announce the inquiry at an afternoon press conference - a fact highlighted by Treasurer Scott Morrison after Mr Shorten's office contacted Westpac in the morning - but the Opposition Leader stopped short of making the announcement.

Well-placed Labor sources said Mr Shorten remained "on board" with the move, which would happen if Labor wins the next election, but the federal Opposition did not want to rush the process, nor be seen to be simply trying to one up Prime Minister Malcolm Turnbull after he rebuked the banks in a major speech at Westpac on Wednesday.