The former South Carolina Gamecocks player met with club officials for dinner on Tuesday night, but Smith said that the plan was to see him again in the next month.
"He's gonna come to Houston at some point later in the month as well," Smith told the Texans' official website. "We talked with him in Indianapolis and spent some time with him there, but that meeting was more rushed. It's a 15-minute block that's back-to-back to back with other guys.
"It was an opportunity for us to really kind of slow the pace down and really get to know the young man, what he's all about, and it really was a good meeting.
"This process is exhaustive so we're going to spend as much time with him and as many other prospects as we can to make sure that we know exactly who they are and what kind of men they are."
Clowney is expected to be a top-10 Draft pick in May.