Michael R. Bloomberg has instructed advisers to draw up plans for a potential independent campaign in this year’s presidential race. His advisers and associates said he was galled by Donald J. Trump’s dominance of the Republican field, and troubled by Hillary Clinton’s stumbles and the rise of Senator Bernie Sanders of Vermont on the Democratic side.

Mr. Bloomberg, the billionaire former mayor of New York City, has in the past contemplated running for the White House on a third-party ticket, but always concluded he could not win. A confluence of unlikely events in the 2016 election, however, has given new impetus to his presidential aspirations.

Mr. Bloomberg, 73, has already taken concrete steps toward a possible campaign, and has indicated to friends and allies that he would be willing to spend at least $1 billion of his fortune on it, according to people briefed on his deliberations who spoke on the condition of anonymity because they were not authorized to discuss his plans. He has set a deadline for making a final decision in early March, the latest point at which advisers believe Mr. Bloomberg could enter the race and still qualify to appear as an independent candidate on the ballot in all 50 states.

He has retained a consultant to help him explore getting his name on those ballots, and his aides have done a detailed study of past third-party bids. Mr. Bloomberg commissioned a poll in December to see how he might fare against Mr. Trump and Mrs. Clinton, and he intends to conduct another round of polling after the New Hampshire primary on Feb. 9 to gauge whether there is indeed an opening for him, according to two people familiar with his intentions.