The secretary of the Nobel Assembly, Thomas Perlmann, said Harriet Wallberg and Anders Hamsten were being asked to step down.
"The crisis of trust is such... that we are going to ask them to leave the Nobel Assembly," he told the Swedish news agency TT.
The pair are former rectors of the Karolinska Institute (KI), Sweden's top medical university, where the scandal coincided with their spells in office.
The affair centres on Italian surgeon Paolo Macchiarini, who in 2011 soared to fame for inserting the first synthetic trachea, or windpipe.
It was a plastic structure seeded with the patient's own stem cells -- immature cells that grow into specialised cells of the body's organs.
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Hired as a visiting professor at Karolinska in 2010, Macchiarini performed three of these operations in Stockholm and five others around the world.
His work was initially hailed as a game-changer for transplant medicine. But two patients died and a third was left severely ill.
Allegations ensued that the risky procedure had been carried out on at least one individual who had not been life-threateningly ill. Swedish police are carrying out an investigation for manslaughter.
Macchiarini is also suspected of lying about his scientific research and his past experience with prestigious medical research centres.
KI dismissed Macchiarini on March 23 and announced the break in an exceptionally blunt statement.
"It is impossible for KI to continue to have any cooperation with Paolo Macchiarini. He has acted in a way that has had very tragic consequences for the people affected and their families. His conduct has seriously damaged confidence in KI," it said.
'Ethical Chernobyl'
An article in the Swedish medical journal Lakartidningen described the case as an "ethical Chernobyl" for KI.
Wallberg's reputation has been tarnished for hiring Macchiarini while Hamsten, her successor as KI's rector, has been accused of failing to grasp the scale of the problem as it unfolded.
Hamsten resigned from KI in February, and the general secretary of the Nobel Assembly, Urban Lendahl, also stepped down from his post. The institute's board has largely been replaced.
Tuesday's announcement came less than a month before the start of the Nobel season, which kicks off this year on October 3, with the medicine award first on the list.
The medicine award is determined by an independent assembly of 50 professors at the KI on the basis of a list of candidates drafted by a five-member panel.
Neither Wallberg nor Hamsten have taken part in the work for the 2016 award, Perlmann said.
The two are being asked to step down as, under the statutes of the Nobel Assembly, they cannot technically be fired.
