The free agent, who was released by New England in February, was undergoing a physical and meeting with Texans officials.
Colvin spent five years with the Patriots and was a member of two Super Bowl winning teams. A foot injury sidelined him for the last five games of this past regular season and the playoffs.
Despite questions about his health, the Texans are interested in the 30-year-old because of his pass rushing ability. He had 52 1/2 sacks in nine seasons with the Patriots and the Bears. The Texans are constantly trying to beef up that part of the defense, an attempt that has mostly fallen short other than the play of Mario Williams last season.
"I coached against him for many years and know he's a fine, fine player," coach Gary Kubiak said. "We are going to keep looking around to see if we can find somebody we think can help us."
Kubiak said he has heard Colvin is healthy, but general manager Rick Smith said he was still awaiting the results of Colvin's physical in Houston before he commented on his health. Last year wasn't the first in which Colvin missed part of the season with injuries. In 2003, he played just two games because of a hip injury.
"From a physical standpoint, as far as my body, everything is well," Colvin told Houston television station KRIV. "Both parties are interested. We need to work something out. If that happens, that's great. If not, we'll move forward."
Smith has known Colvin since he recruited him out of high school to play at Purdue.
"He's a good football player who is still available and so we decided to bring him in," Smith said. "He adds a pass rush type of element for us, if we are able to add him or are so inclined to do so. That's what it is. It's an exploratory type of visit. We want to get a look at him and see how healthy he is and continue to talk to him."
Colvin said several teams are interested in talking to him.
"It's just a matter of teams being committed to who I am as a player. If we can get that done, regardless of where it is, I think I am on board."