The 6-foot-5, 307-pound Smith enters the NFL after his junior season, with analysts touting him as one of the top offensive tackles in the draft.
NFL teams are allowed up to 30 in-house visits with out-of-town prospects before the draft. The visits are often used to double-check medical information or to conduct one final interview before placing a grade on a prospect.
Another reason the Patriots might be taking a closer look at Smith is that Matt Light, their starting left tackle since 2001, is an unrestricted free agent.
The Patriots have third-year pro Sebastian Vollmer returning at right tackle, and Vollmer also has experience at left tackle. That flexibility gives the Patriots options when assessing this year's tackle class.
Mike Reiss covers the Patriots for ESPNBoston.com. ESPN NFL Insider Adam Schefter contributed to this report.