Prime Minister and self-labelled feminist Pedro Sánchez is expected to appoint a women-majority cabinet, in contrast to the male-dominated executives of ousted PM Mariano Rajoy.
Women will take the deputy premiership, and the economy and finance portfolios.
Mr Duque, 55, last went to space in 2003 as part of an International Space Station (ISS) mission.
An aeronautical engineer with three children, he is prone to quoting the late British science fiction writer Arthur C Clarke, Spanish media report.
Mr Duque was selected by the European Space Agency's astronaut corps in 1992 and became the first Spaniard to travel to space in 1998, when he joined Nasa's STS-95 mission from Cape Canaveral. Mr Duque served as a mission specialist aboard the Space Shuttle Discovery on the nine-day mission.
He and three other STS-95 crew members were awarded the Princess of Asturias Award for international cooperation in 1999, which called them "the architects of the pacific exploration of the universe".
In 2003, he took part in the 10-day Cervantes ISS mission as a flight engineer on the Russian Soyuz-TMA.
From 2011 he headed the ESA's Flight Operations Office in Munich, Germany, and in 2015 "returned to astronaut duties and full flight status", according to a profile on the ESA website.
His official title will be minister of science, innovation and universities, El País newspaper reports.
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