A new poll from Bloomberg shows Trump leading his Democratic rival by 2 points.
Other polls show Clinton still holding the lead, though not by much. Clinton leads Trump by just 1.5 points, according to a Real Clear Politics poll average, down from 2.4 points a day ago. As recently as last month, this spread was considerably wider, with Clinton leading Trump by as much as 7.6 points.
FiveThirtyEight's forecast pegs Trump's chance of winning at 51.9 percent to Clinton's 48.1 percent.
Individual polls reflect just how tight this year's race stands ahead of the debate on Monday.
Among likely voters, Clinton leads Trump 46 percent to 44 percent, according to a new Washington Post-ABC News poll.
In a Quinnipiac University national poll out Monday, Clinton has the support of 44 percent of likely voters, while Trump stands at 43 percent.
The deadlocked polls underscore just how pivotal the debate, which will be the first of three, could be in influencing the outcome of the Nov. 8 election. A full 50 percent of likely voters indicated in a Reuters/Ipsos poll that the debates will help them decide whom they choose at the polls.