Neither Trump nor Clinton has secured their respective party's nomination, but both candidates cemented their leads in this week's Super Tuesday contests.
There are currently two schools of thought, Richardson said. One believes that Trump will be the Republican nominee, and Clinton will best him in a general election by a wide margin. But others — Richardson included — think the businessman won't go down so easily.
"We've got to be very careful because Trump has tapped into a negativity, a populism that is out there, and I think we have to work extra hard" to attract young voters and turn out the party's base, the 2008 Democratic presidential contender told CNBC's "Squawk Box."
Clinton faces the challenge of not just defeating Vermont Sen. Bernie Sanders in the Democratic primary, but overcoming him in a way that allows her to rally his "significant coalition" of supporters, Richardson said.
He said he believes Clinton can ultimately do just that and go on to beat Trump.