The site selection committee said it was headed into its next phase of deliberations by entering into "further discussions" with SMU, according to a Thursday statement by committee member Donald L. Evans, former commerce secretary.
Southern Methodist is competing with two other finalists, Baylor University and the University of Dallas. SMU is the first lady's alma mater, and Baylor is near the couple's ranch in Crawford.
Southern Methodist President R. Gerald Turner said he was told the discussions would be "exclusive" with his school but provided no details about what might need resolution before a final decision, expected in a few months.
"So obviously, although we're not announcing that it is coming here; this is as good of an announcement as we could give you," Turner said at a campus news conference Thursday. "This is the best stage that we could be in at this point in time."
Tommye Lou Davis, director of Baylor's Bush Library Project, said the committee told her Thursday that Baylor had not been eliminated. Baylor, the world's largest Baptist university with 14,000 students, will "continue to focus on enhancing our position," she said.
"We won't lose hope until they've made a final decision," she said.
University of Dallas President Francis M. Lazarus released a statement Thursday saying that officials of the 3,000 student Catholic school in Irving "know that no official decision has yet been made."
The library is expected to cost at least $200 million and be financed with private donations.
Texas already has two presidential libraries: the George H.W. Bush Library at Texas A&M University in College Station, and the Lyndon Baines Johnson Library at the University of Texas at Austin.