A spokesman for Trump says the businessman and television host changed his affiliation to preserve his option to seek the presidency in 2012.
Special Counsel Michael Cohen said Friday that Trump could enter the race if Republicans fail to nominate a candidate who can defeat President Barack Obama.
He said Trump probably would use his substantial wealth to even the playing field with Obama's re-election campaign.
Cohen said Trump's commitment to hosting TV's "The Apprentice" will keep him from doing anything until May, when the show's season wraps up.
He said Trump filed his voter registration paperwork Thursday.
