Both people spoke on condition of anonymity because they were not authorized to make the announcement public. Fossella was expected to make the announcement Tuesday.
Fossella, 43, has admitted to fathering a daughter with a Virginia woman.
The congressman's secret relationship with the woman, Laura Fay, was revealed after he was arrested for drunken driving May 1. Fossella was stopped after running a red light, and he told officers he was going to see his sick daughter, according to police.
Fossella is married with three children. The family lives on Staten Island.
He has served in Congress since 1997, representing Staten Island and part of Brooklyn. He is the only Republican member of Congress from New York City.
It was Fay who got him out of jail after the arrest. She is a former Air Force lieutenant colonel and worked for a time as a liaison to Congress.
After his arrest, police said Fossella's blood-alcohol level was twice the legal limit, and he could face a mandatory five days in jail if convicted. A court appearance on the drunken driving arrest is scheduled for next month.
After the relationship was revealed, Fossella said he had no immediate plans to resign, but the disclosures were considered by many as a crippling blow to the career of a lawmaker once viewed a potential candidate for mayor of New York City.
He faced a surprisingly tough re-election challenge in 2006, and Democrats have been hoping to unseat him this year. After the admissions, Fossella got little public support to remain from leaders of his own party.
Fossella was elected to Congress in 1997 in a special election to replace Rep. Susan Molinari, who resigned. His socially conservative positions squared nicely with his largely Catholic district. He serves as a member of the House Committee on Energy and Commerce.
His work in Congress shifted dramatically following the Sept. 11, 2001, terror attacks. Hundreds of Staten Island residents died in the attacks, and Fossella became a prominent advocate for families of those killed.
As more recovery and rescue workers got sick after toiling at the ground zero site, Fossella pushed for Washington to pay for their health care - an effort that met with short-term success, but no long-term program.