Houston, which traded quarterback Matt Schaub in the offseason, has a major question mark under center, having to decide from among Ryan Fitzpatrick, Case Keenum and rookie Tom Savage.
Johnson is looking to win now and appears to be unwilling to be a part of a rebuilding project, despite the Texans taking defensive end Jadeveon Clowney with the No. 1 pick in the draft.
"I just choose not to talk publicly about it," Johnson said. "It's in-house and that's the way I choose to keep it. I'm not a big media guy, so I won't -- you know, I refuse to talk about it. Training camp's a few weeks away, so we'll see what happens."