Yes we do, going by Five Thirty Eight's We’ve Got Some New Polls For Bloomberg’s Potential Campaign. They Aren’t Great. (links from the article, emphasis on numbers mine, I split the paragraph to distinguis between polls):
Shortly after news broke that Bloomberg might run, Morning Consult ran a quick poll that found he would pull 4 percent of the national primary vote. That’s about where he was polling before he initially said he wouldn’t run, back in March: not terrible, but hardly strong enough to pose a serious threat. And even though Bloomberg’s advisers have said he would actually skip the first four primary states if he runs — a truly unorthodox strategy — two early-state polls that also asked about him this week found that he barely registered there.
Only 2 percent of likely Democratic primary voters in New Hampshire told Quinnipiac that they would “definitely vote” for Bloomberg, although an additional 37 percent did say they would “consider voting” for him.
And in a Monmouth poll of Iowa, Bloomberg earned the support of less than 1 percent of likely Democratic caucusgoers.
And it might be especially hard for Bloomberg to increase his support considering his lackluster favorability numbers. In that Morning Consult poll, his favorable rating was 31 percent and his unfavorable rating was 25 percent.