Story highlights The latest USA Today/Suffolk University finds little room for a Michael Bloomberg White House bid

If the former New York City mayor entered the race, he would likely siphon off almost twice as many Bernie Sanders supporters as Donald Trump supporters

Washington (CNN) Michael Bloomberg has a very slim chance of winning the presidency should he declare a bid, but he could cost Bernie Sanders the White House in a hypothetical three-way matchup with Donald Trump, a new poll finds.

USA Today/Suffolk University poll released Wednesday found Trump slightly edging out Sanders in a head-to-head matchup, 44% to 43%, within the poll's margin of error. But if the former New York City mayor entered the race, he would likely siphon off almost twice as many Sanders supporters as Trump backers -- leaving Trump at 37%, Sanders at 30% and Bloomberg with 16%.

Bloomberg said two weeks ago that he was considering a White House bid.

"I find the level of discourse and discussion distressingly banal and an outrage and an insult to the voters," Bloomberg told the Financial Times, adding that the public deserved "a lot better."

Sources familiar with Bloomberg's considerations have told CNN that he would consider spending $1 billion of his own money and would only enter if Trump or Ted Cruz won the Republican nomination and Sanders was the Democratic nominee.

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