The agency posted a request June 24 for bids for studies on what steps would be needed to make the crown safe, the New York Daily News reported.
The statue was closed to visitors immediately after the Sept. 11, 2001, terrorist attacks. The pedestal reopened in 2004, but the crown, reachable only by a narrow staircase, remains off limits.
A spokesman for the service said the study would be completed next year, and the crown may never reopen.
"We are asking the firm to answer two questions," said Darren Boch. "Is there a way to make changes to the structure itself to make it comply with safety codes? If they say, no ... they would look at a way to minimize the risk."
Rep. Anthony Weiner, D-N.Y., who has been pressing to reopen the crown, called the steps so far "a dramatic breakthrough."