"Obviously this will have to be decided in the coming days, perhaps before I return to Brazil, whether he wants his name submitted to the Senate for the embassy or not," Bolsonaro told reporters in Tokyo where he is on an official visit.
"In my opinion, (the best) is that he stays in Brazil... to pacify his party and pick up the pieces so to speak," President Bolsonaro said.
His son's name has yet to be submitted to the Senate for approval as ambassador to Washington and a recent political storm surrounding the PSL has likely reduced his chances of being confirmed.
Bolsonaro said he would consider appointing Nestor Foster, currently Brazil's charge d'affaires in Washington, in place of Eduardo.
The president's remarks come after his son took over the leadership of the PSL in the lower house of Congress on Monday in a bruising struggle for control of the party.
The struggle stems from an increasing rift between PSL founder Luciano Bivar and President Bolsonaro, who used the previously small party as the platform for his presidential campaign and helped transform it into the second largest in the Brazilian Congress.
The battle for control is not over yet.
The national leadership of the PSL met on Tuesday at the party's headquarters to discuss the suspension of around two dozen lawmakers who backed the overthrow of Delegado Waldir as party house whip, including Eduardo Bolsonaro. If suspended they could lose their seats in Congress.
The Brazilian president had said he would appoint his son to the U.S. embassy in early July, a day after Eduardo turned 35 - the minimum age for the job.However, although the U.S. government has already given the "agrement" - a kind of acceptance from the host country - Eduardo's name has still not been submitted to the Senate for approval due to a lack of support to guarantee his confirmation.