This is a delicate subject. While the potential for discrimination is rarely an issue in this context, directly inquiring about the existence of a disability is not appropriate. A private academic conference may give you an opening to mention various explanations for poor performance without implying that any certain one applies. You may also provide the student with information on the various campus resources available for assistance such as ACE, Student Support Services, and the Disability Resource Center.
If the student initiates the subject and is receptive, of course you are free to discuss the disability issue in detail. Alternatively, you could address learning disabilities in a general way with the whole class as a follow-up to an exam, and share the DRC contact information. The DRC will provide screening and testing services for students who cannot obtain the services through other agencies.
Kentucky residents can obtain assessment through the Office of Vocational Rehabilitation on a sliding scale basis. Students can also obtain evaluations through the rehabilitation offices in their home states. It is in their best interest to seek evaluations through these agencies because they offer additional services that the University cannot provide. Some students are eligible to receive testing at no cost, depending on their financial situation. The University does not provide (or cover costs) for outside diagnostic testing, but the DRC office can refer to an agency in the community. On a limited basis, the DRC will provide screening services. However, as noted earlier the Vocational Rehabilitation office provides more comprehensive services and would be a greater benefit to the student.