Bolsonaro, a far-right nationalist, left Brazil for Florida on Friday after losing to leftist President Luiz Inacio Lula da Silva in Brazil's most fraught vote in a generation.
Bolsonaro's U.S. trip insulates him from any immediate legal jeopardy in Brazil, where he is under investigation in at least four criminal probes.
Under Brazil's constitution, a sitting president can only be arrested if he is convicted by the Supreme Court.
From September, Lula will be able to install his own prosecutor general, who has the power to charge Bolsonaro if his cases remain with the Supreme Court.
Bolsonaro also faces 12 requests for investigation at the Superior Electoral Court (TSE) for baseless claims Brazil's electoral system is liable to fraud, as well as alleged abuses of power for granting economic benefits to win votes.