General manager Rick Smith has made eight trades in six drafts with the Texans.
He's not opposed to adding to his total in 2013.
"In this draft, there are a lot of players that we like in the mid-rounds, and I think some players that can impact your football team," Smith said on Tuesday at Reliant Stadium. "We are always open to trades, moving up and moving back. We've done that and certainly are willing and open to doing that again this year as well."
Smith has made at least one trade in five of his six drafts with the Texans, the lone exception coming in 2009. He made one trade in 2012, two in 2011 and three in 2010.
Six of Smith's eight draft-day trades have been moves down that acquired additional picks. He has traded down in the first round once, moving from 18th to 26th in 2008 to select tackle Duane Brown, but never out of the first round completely.
With the 27th overall pick in this year's draft, the Texans are in a position to let the first round come to them on Thursday. Smith said Tuesday that they might even trade up.
"I'm confident there will be a player there that we like (at 27)," Smith said. "I'm confident of that. Am I confident we won't move? I don't know. There's a dynamic that's involved in the process during draft day. Just depending on the way that the board falls, there may be a player that we've got a certain value on that's all of the sudden available and we may want to go up and get him. Correspondingly, there's teams that want to come up and grab players where we are."
The 27th overall pick has been traded in four of the past 10 drafts.
"I do think that the 27th spot is an attractive spot from the standpoint that historically, you look back and there are teams that come back into the draft in the latter part of the round if a player is there they have targeted earlier," Smith said. "So I think we'll have some flexibility, but I am confident if we don't (trade), we'll get a good player. But we'll be open."