The Texans have the number one overall pick of the upcoming Draft, and with a quarterback high on their list of needs, there is a good chance that they will select one with either of their first two picks.
He told the Houston Chronicle: "If I am still available in the second round, they're going to get even more of a chip on my shoulder than there already is. But absolutely, I'd love to play for the Houston Texans.
"They have a great team. They have a great offensive line and one of the best tackles in the game in Duane Brown. I've also thrown to Andre Johnson before, so the timing should be OK.
"I just want to come out and show teams that I can be their franchise quarterback and who I want to be. It's kind of like a mission."
Most NFL mock drafts have Carr down as being the fourth quarterback to be picked this year, with many predicting that he will end up as the choice of the Minnesota Vikings.