Vitter will face reporters in a Monday evening press conference.
Vitter, R-Louisiana, apologized to constituents last week for "a very serious sin in my past" after his number turned up in telephone records of the service run by Deborah Jeane Palfrey, the "D.C. Madam" now facing money laundering and racketeering charges.
The 46-year-old lawmaker, who is married and has four children, has not been seen on Capitol Hill since his July 9 admission. He is scheduled to hold a news conference in his hometown of Metairie, La., at 5 p.m. (6 p.m. ET)
Before winning his Senate seat, Vitter represented New Orleans' northern and western suburbs in the House of Representatives from 1999 to 2004. In the Senate, he was one of the top backers of the failed "Marriage Protection Amendment" - which would have banned same-sex marriages - and serves as the southern regional chairman of former New York Mayor Rudy Giuliani's presidential campaign.
In an e-mail to supporters Friday, Vitter apologized for "letting you and others down" and thanked supporters for their thoughts and prayers.
Pornographer Larry Flynt's Hustler magazine claimed credit for exposing Vitter's connection to the escort service, saying Vitter came clean after a journalist working as a paid consultant for the magazine turned up the senator's number in phone records released by Palfrey.
Federal prosecutors say the business, Pamela Martin and Associates, was involved in prostitution, but Palfrey says she operated a legitimate escort service.
Sen. Jon Kyl, R-Arizona, told CNN's "American Morning" that Vitter would be returning to the Senate - "I just don't know when" - and said talk of his resignation was "premature."
"Frankly, I don't know what it is that he has apologized for," Kyl added.