HOUSTON -- Astros general manager Jeff Luhnow said Monday the organization is looking for a "face of the franchise" with the first pick in this week's 2013 First-Year Player Draft, but that there are still "about five" players under consideration for the pick.

"We have a handful of players left we're seriously considering," Luhnow said. "The number could go up or could go down, but ultimately, it has to go down to one. We feel good that those handful are players who can have a significant impact on our franchise."

The 2013 First-Year Player Draft will take place Thursday through Saturday, beginning with the Draft preview show on MLB.com and MLB Network on Thursday at 5 p.m. CT. Live Draft coverage from MLB Network's Studio 42 begins at 6 p.m., with the top 73 picks being streamed on MLB.com and broadcast on MLB Network. Rounds 3-10 will be streamed live on MLB.com on Friday, beginning with a preview show at 11:30 a.m., and Rounds 11-40 will be streamed live on MLB.com on Saturday, starting at noon.

MLB.com's coverage includes Draft Central and the Top 100 Draft Prospects list. You can also keep up to date by following @MLBDraft on Twitter. And get into the Draft conversation by tagging your tweets with #mlbdraft.

The Astros have the first pick for a second straight year. Luhnow and amateur scouting director Mike Elias said they still don't know which player will become Houston's fourth No. 1 overall selection.

"We're meeting here all the way through Thursday morning," Elias said. "The decision will be made some time Thursday morning. You want to get as much info as possible and hear as many voices to inform your decision. We don't feel any need or advantage to making the decision early."

Oklahoma pitcher Joanathan Gray and Stanford pitcher Mark Appel are widely considered to be likely candidates for the top pick.

This is Elias' first season as the Astros amateur scouting director. He'll basically run the Draft for the organization beyond the first round, just another responsibility as he prepares for his first major moment at the helm.

"It's been a big change," Elias said. "It's the first year I've had to take on all the duties at once. Previous to this, I'd done almost every part of the job in some capacity. Day-to-day management, manage cross-checkers, scouting or decision-maker -- I'd done those things -- but now you're involved in all of them at once.

"You scout these players and have your own personal opinion, but now there's this executive hat that you also put on. Your executive opinion when you hear the different voices often differs from what you thought personally as a scout."

Elias said he relied on the team's regional player camps to prepare him. The Astros observed hundreds of players and interviewed them at team-specific camps in Houston, Atlanta, Southern California and Florida this spring.

"That's a very big part of how I work," Elias said. "They're something the Astros have done previously, and I did it with the Cardinals. It's an opportunity to get talent from the hottest regions onto one field for all our scouts and allows to answer specific questions. So. Cal, Houston, Atlanta and Florida are the four hotbeds of the country from an amateur baseball perspective."

Elias, 30, was a special assistant to the general manager last year and was also involved in St. Louis' Drafts while working under Luhnow between 2007-11.

While the focus has been on Houston's No. 1 overall pick, Luhnow stressed that the franchise's future relies on picks made all the way through Round 40.

"We had a seminal Draft last year and took a huge step forward because of our drafting depth," Luhnow said. "We have that opportunity again this week. If we don't pay attention to the rest of the Draft, we're going to fail miserably. Being thorough, 1-40, is how we will catch up as an organization."