Correa, 6-foot-4, 190 pounds, became the highest-drafted Puerto Rican high school player in Major League history by going No. 1 overall to Houston.
He has signed to play at the University of Miami, but it certainly appears he's on the verge of starting his pro career.
"We're going to bring him in here on Thursday, and you guys [the media] are going to get a chance to meet him and we're going to get a chance to sit down and talk with him and his family, and hopefully that will move quickly at that point," Luhnow said.
Once signed, Correa would report to extended spring camp at the club's complex in Kissimmee, Fla. -- the same place where Correa blew the Astros away in a May 27 workout -- before beginning his career with the Gulf Coast League Astros at the same site.
Luhnow said he expected to sign all of the Astros' top 11 picks in the first 10 rounds, including No. 41 overall pick Lance McCullers Jr., a pitcher from Tampa, Fla. Houston can spend a combined $11.177 million on its first 11 picks without getting penalized.
The Astros have until July 13 to sign their Draft picks.
"We feel pretty good that we're going to sign all 11 players we drafted," Luhnow said.
Luhnow said he expects signing McCullers -- who has a signing bonus of $1.258 million -- will take a bit longer than some other players.
"There's a little more work to do there," he said. "We're going to wait until the Draft is over and start to come up with a plan there. I like to take more time with pitchers. They need some rest [because] they've had a long spring. He's obviously had a successful spring, but it would wear on anybody. You have to give him rest.
"There's no urgency. As with Correa and any of these types of players, we want to get that pick out quickly so we can benefit."
Luhnow said the team could announce a flurry of signings on Thursday.
"We've got a pretty good feel for what players are asking for and we have a very good feel for what recourse we have," he said. "Where there's a match, we're going to have to execute it immediately. Our scouts are heading back [Wednesday], and the first task of business is signing the players they drafted."