Bolsonaro senior said Thursday his son's friendship with Trump's children and his ability to speak English and Spanish made him "the right person" for the job.
The president said the nomination "would be the ideal message to Washington".
Eduardo Bolsonaro, now a federal congressman, told reporters he would accept the role if nominated. "It is not nepotism, I would never do that", Bolsonaro said on a live social media broadcast on Friday. The ambassadorship has been vacant since January 1, when Jair Bolsonaro took office.
Despite being a congressman in the lower house, the third of Bolsonaro's four sons shadows his father on official trips overseas, including the recent G20 summit in Japan. "Eduardo Bolsonaro's nomination for ambassador is unacceptable", tweeted Senate opposition leader Randolfe Rodrigues.
In Brazil, nomination to any ambassador's position is made by the president, but the candidate must be questioned by the Senate and approved by both the Senate and the House.
Mr Bolsonaro uses several of his members of the family as reliable advisers.More news: Roger Federer vs. Rafael Nadal
More news: Hundreds of thousands plan raid on Area 51 to 'see them aliens'
More news: Trump hits out at China over slowing agricultural purchases
When asked by reporters about his qualifications for the position, Eduardo Bolsonaro said he had been in a foreign exchange program where he "fried hamburgers in the United States, in the cold in Maine" and "in the cold in Colorado, on a mountain there".
Eduardo Bolsonaro also noted that he heads the foreign relations commission in the lower house of Congress.
Eduardo, now a member of parliament, accompanied his father to a private meeting with Trump during a diplomatic visit to Washington in March.
Mr Bolsonaro used to be elected final year after a a hit campaign he acknowledged had been inspired by Donald Trump.
Eduardo turned 35 on Wednesday, Brazil's minimum legal age for ambassadorships. The ambassador from the previous administration left the position on June 3.
Eduardo would must resign as a congressman if he did occupy the discipline of ambassador.