ESPN's Todd McShay and Mel Kiper both have the Texans selecting defensive end Jadeveon Clowney with the top pick in their final mock drafts.
Last week, Texans general manager Rick Smith said he knew whom he would take at No. 1 if the team keeps the pick.
"I know the order of our board," Smith said. "If we select first, it's a unique opportunity to be the first pick. If we do select there, I know who we feel good about there. If we move, then obviously there are variables that come into play at that point."
If the Texans were to trade the pick, team sources have told ESPN's Ed Werder that it probably wouldn't happen until they are on the clock.
The Texans first suggested an interest in trading the pick in early January, after hiring Penn State's Bill O'Brien as coach to replace Gary Kubiak.
"Maybe we'll trade down and still get a quarterback that can do the job and get an outstanding defensive player," team owner Bob McNair said then. "It's an exciting time. Everything's a moving target. Lot of different pieces."
This is the third time in franchise history that the Texans have had the first overall pick and the first time Smith has presided over one. In 2006, after selecting Mario Williams first overall, Charley Casserly stepped down as general manager. The Texans already had hired a coach for that season -- Kubiak.
Kubiak was fired with three games remaining last season, his eighth with the team.
Information from ESPN.com's Tania Ganguli was used in this report.
Texans Trade Would Come While On The Clock
Ed Werder talks about if and when the Texans would decide to trade away the number 1 pick in the 2014 NFL Draft.