It hopes to complete fund-raising by Sept. 10, when dedication of the first phase of the memorial in Shanksville, Pa., is scheduled.
Sullivan said that work on the memorial had come in under budget so far. That means that if the fund-raising goal is reached, the project will include a tower marking the entry to and exit from the site on Route 30.
The "Tower of Voices" is designed to house 40 wind chimes, and would be illuminated at night to commemorate the 40 passengers and crew who died on Flight 93, according to the architects.
The first phase of the memorial includes a ring road leading to the site, a memorial plaza, and a parking area.
President Obama is expected to visit the Flight 93 Memorial on Sept. 11, and Vice President Biden is scheduled to attend the dedication the day before.
Gordon Felt, president of the Families of Flight 93, said in a statement that "their visit underscores the importance of the Flight 93 National Memorial and the progress so many are making in creating it."
United Airlines Flight 93 was traveling from Newark, N.J., to San Francisco on Sept. 11, 2001.
The 9/11 Commission found that the hijackers likely wanted to crash into the White House or the Capitol building but downed the jet in Pennsylvania as passengers fought back.