An announcement will be made as early as Thursday, according to the congressional figures close to Corzine, also a Democrat. They spoke on condition of anonymity because the official announcement had not yet been made.
Menendez would be the first minority member to represent New Jersey in the Senate, and would be the body's third sitting Hispanic senator.
When asked about his prospects after Wednesday's House Democratic Caucus meeting, which he chairs, Menendez told The Associated Press that the decision was Corzine's to make and he was waiting for the announcement like everyone else.
"I stand ready to serve," Menendez said.
Corzine's term expires in 2006 and state law lets the governor fill Senate and House vacancies. Corzine was elected governor last month.
The only Republican candidate for the 2006 Senate race thus far is state Sen. Tom Kean Jr., the son of Thomas Kean, the former governor and chairman of the Sept. 11 commission.
Dozens of Hispanic groups lobbied heavily for Corzine to select Menendez, the son of Cuban immigrants.
Menendez, 51, has a $4.1 million campaign war chest to run for a full Senate term in 2006.
In an interview with The Associated Press last month, Menendez said he believed he would be an effective senator because "I have walked the shoes of the average New Jerseyan."
"I have lived in the state virtually my entire life and I have dedicated my adult life to public service within the state," he said. "As someone who came from immigrant parents and was the first to go to college from my family, I understand the hopes and dreams of aspirations of people."
Menendez entered politics when he was 20, winning a seat on the Union City, N.J., school board while attending St. Peter's College. While on the school board he learned that the city's mayor, William Musto, was involved in illegal activities and he testified for the federal government against Musto.
During Musto's trial, Menendez received death threats and wore a bulletproof vest. Musto ultimately was convicted and sentenced but he still won re-election over Menendez in 1982. When Menendez ran again in 1986, he won. In 1987, he ran for state Assembly and won, and he was later elected to the state Senate.
In 1992, he ran for Congress and won a House seat in that first attempt.
Menendez's parents left Cuba before he was born and settled in Union City, where he grew up in a tenement with his two siblings. Menendez always wanted to be a U.S. senator, said childhood friend Donald Scarinci, a New Jersey lawyer.
"Bob is going to be the best U.S. senator that New Jersey has ever had, and he'll show that ability very early," Scarinci said. "Bob was always one of the smartest people that I would talk to, he was very full of ideas and so full of enthusiasm and had an excitement about government that was contagious."
"We grew up in the shadow of Vietnam and then, getting involved in government was a way to change the world," Scarinci added. "It was something we all talked about and something we all wanted to do eagerly."
Menendez has been vocal on homeland security measures, pressing for stricter laws to make the state's chemical plants safer from a terror attack. He wrote the Bioterrorism Protection Act and the United States Security Act to ensure that the country has the resources and tools it needs to respond to terrorism.
He is divorced and has two grown children.
New Jersey has not elected a Republican U.S. senator since 1972, but Republicans hope to reverse that streak and feel Kean Jr. has a terrific chance of winning next year.