Booker -- a Democrat who has said he intends to serve the remainder of his second term as mayor of New Jersey's largest city -- filed documents Tuesday with the Federal Election Commission for "Cory Booker for Senate," The Hill reported.
Lautenberg, who turns 90 in 2014 and is the oldest current member of the Senate, has not said whether he will seek a sixth term.
Rep. Frank Pallone, D-N.J., may also be considering a Senate run, The Star-Ledger of Newark reported.
Booker is Newark's third black mayor. He grew up in a North Jersey suburb and moved to the city after attending Stanford, Yale and Oxford University.
In a recent Fairleigh Dickinson University poll, 42 percent of respondents said they would prefer Booker and only 20 percent backed Lautenberg -- who held the seat from 1982-2001 and then returned to the Senate after replacing incumbent Sen. Robert Torricelli as the Democratic nominee in the 2002 election.