Shane Lechler has been the Texans punter since 2013.
Head coach Bill O'Brien hopes the Pro Bowler returns to the Texans in 2017.
"He's a guy that we would like to have back here," O'Brien said of the 17-year veteran. "Hopefully we can work something out."
Lechler will be a free agent in March. He was one of the 10 best in the NFL this season in yards per punt (47.5) and punts downed inside the 20 (30).
"He did a good job for us," O'Brien said. "I think everybody knows how I feel about Shane. He's a great pro. He's had a great career here."
In addition to another strong year punting, O'Brien pointed out the value of Lechler's leadership. Lechler was a team captain for all 16 regular season games and both playoff matchups.
"He's a leader in the locker room, he's a captain," O'Brien said. "Means a lot to me personally. He had a heck of a year. Did the things that we asked him to do. It was good to see that."
Lechler pinned the Raiders inside the 20 a Texans playoff record four times in the Wild Card victory.