Clinton will be shown around Christiansborg, the seat of Denmark's parliament, before one-to-one talks with Rasmussen, the PM's office confirmed in a press statement.
No further details of the meeting have been released.
The former president, who led the United States government for two terms from 1993 to 2001, has already arrived in Denmark, newspaper Børsen reports.
He is scheduled to give a keynote speech at a summit held by the Presidents Institute foundation in the Danish capital on Wednesday, with up to 3,000 European leaders expected to attend.
Rasmussen is back in Copenhagen after last week visiting Germany, Spain and Portugal to speak to European government leaders about the future of the European Union after Brexit.