In 1986 he became the second sitting member of Congress and the first member of the House to travel to Space.
He was a payload specialist on the space shuttle Columbia, from 12-18 January that year — 10 days before the Challenger disaster grounded the fleet.
Mr Nelson would be the second former congressman in a row to lead Nasa, with the president expected to formally announce his choice as soon as Friday, according to The Washington Post.
He is a longtime advocate for the agency and will be the first administrator to have been to space if his nomination is approved by the Senate.
The selection of Mr Nelson will potentially disappoint some who had hoped Mr Biden would nominate a woman to lead the agency that intends to put the first woman on the moon.
“It’s time for a female administrator,” Wayne Hale, former Nasa space shuttle programme manager, wrote on Twitter. “Plenty of qualified candidates.”
The Post also reports that the White House is strongly considering Pamela Melroy, a former Nasa astronaut and a retired Air Force colonel, as deputy administrator, but a final decision has not been made.
One woman flagged for the top job by observers on Twitter is Lori Garver, former deputy administrator of Nasa during the Obama administration.
In the past, Mr Nelson spoke out strongly against former president Donald Trump’s pick to lead Nasa, Jim Bridenstine, a one-term member of the House for Oklahoma.
“The Nasa administrator should be a consummate space professional, who is technically and scientifically competent, and is a skilled executive,” he said at the time.
“This committee has heard me say many times: Nasa is not political. The leader of Nasa should not be political. The leader of Nasa should not be bipartisan.”
In 2017, Mr Bridenstone was confirmed in a narrow 50-49 vote in the Senate.
Mr Nelson would take the helm at the agency as it struggles to keep the Artemis programme on track to put the first woman and the next man on the Moon by 2024.
Artemis 1 is scheduled to launch near the end of the 2021 and perform an un-crewed orbit of the Moon.
“I cannot think of anyone better to lead Nasa than Bill Nelson,” Senator Marco Rubio said in a statement on Thursday. “There has been no greater champion, not just for Florida’s space industry, but for the space programme as a whole than Bill.”
“His nomination gives me confidence that the Biden Administration finally understands the importance of the Artemis program, and the necessity of winning the 21st Century space race,” Mr Rubio added.
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