The country's parliament, which dismissed the outgoing center-right government of Emil Boc on October 13 with a vote of no confidence, was expected to vote on the nomination later in the day.
The ruling coalition had imploded on October 1 with Boc's dismissal of a Social Democratic cabinet minister over comments he made about possible electoral fraud.
The country's voters go to the polls in November to elect a president, with Basescu currently regarded as the front-runner.
Currently adviser to the head of the Romanian central bank BNR, Croitoru is a former Romanian representative to the International Monetary Fund (IMF).
President Basescu also said the IMF had postponed a mission to Bucharest until "after parliament approves a new government."
IMF representatives were expected to visit Romania in coming weeks to review progress under a $30 billion aid accord.
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