Booker, who leads the state's largest city, also told CBS' "Face the Nation" that he's also thinking about running for the U.S. Senate.
He said he has to decide on a gubernatorial bid in the next couple of weeks out of respect for his party and the other Democratic candidates who'd like to take on the outspoken Christie.
"I've got to give my party and be a part of my party's push forward, whether it is with me as a candidate or with supporting other candidates for that office," Booker said.
Speculation about the political future of the 43-year-old Booker has been high for much of his second term as mayor. He had planned to announce his intentions shortly after the presidential election, but those plans were put on hold as he dealt with Superstorm Sandy and its aftermath.
Christie has announced he's for re-election. Recent public opinion polls have ranked Booker as the Democrat who could come closest to beating the GOP incumbent, but they also show strong support for Christie.
As for the Senate, the seat held by 88-year-old Democrat Frank Lautenberg is up in 2014. Lautenberg has not announced plans to step aside.
Booker is known perhaps as much for his large Twitter following of more than a million users and interaction with residents as for his governing. He once shoveled snow during a storm and invited people who were without electricity during Sandy to spend time at his home.
Booker is in the midst of a week of living on food stamps, a challenge that other politicians have taken on in recent years to highlight the difficulty of relying solely on government aid for nutrition.