Nicholas Brady, expected to be named by President Reagan to replace Secretary of the Treasury James A. Baker III when he leaves to take over Vice President George Bush's presidential campaign, would continue in that position if Bush wins the election.

Baker's long-awaited departure is likely to come next week, administration officials said Friday, once the White House receives assurances from congressional leaders that Brady can be confirmed quickly by the Senate."It's not done. It's getting done fast," said a former White House official close to Baker and the Bush campaign. "It all relates to if Brady can get in quickly."

Brady, a longtime friend of Bush who headed the presidential commission that examined last October's stock market crash, would join Baker, who would like to be secretary of state, and Reagan's recent nominee as attorney general, Richard Thornbourgh, as Reagan Cabinet officials who are all but certain to assume top positions in a Bush administration.

There is a remote chance that Brady's appointment could be derailed, but only if it appears that a prolonged background check of his extensive financial holdings would significantly delay his taking the reins of the Department of the Treasury, officials said. In that case, Deputy Secretary of State John Whitehead is the top candidate to be named to the post just for the Reagan administration's final few months because he already holds a high office and could be named acting Secretary while awaiting Senate confirmation.

Baker, who has recommended Brady as his replacement, is concerned that financial markets might react negatively if there is a lengthy period between his departure and the time his successor takes office.