Parker, running a lightly funded campaign focused on a vast expansion of passenger rail systems in Virginia, is polling only 2 percent in statewide polls.
But in a close race between Allen and Webb, her withdrawal could determine whether Republicans retain their Senate majority.
Parker said in a telephone interview with The Associated Press that her campaign has asked Allen's campaign to commit to new funding for train systems and to swiftly install a new accounting system at the Pentagon.
"We are trying to negotiate the best deal to get high-speed rail in Virginia immediately or as soon as possible," Parker said.
She said her campaign had left a telephone message Thursday for similar discussions with Webb's campaign.
Parker said she had not committed to withdrawing from the race and that she had set no timetable for deciding whether to back either Webb or Allen.
There was no immediate reply to AP telephone calls seeking comment on Parker's statement from Webb and Allen campaign officials.