The Titans have the No. 2 overall pick in the draft after a 2-14 campaign last season. The team could select one of the two top quarterback prospects available: Heisman Trophy winner Marcus Mariota of Oregon and Florida State's 2013 Heisman winner Jameis Winston.
"We like Zach, and I think Zach has the tools to play and start in the league," Webster told the Tennessean. "We've said all along that this is a part of this process, and we have to do our due diligence all the way through. Zach knows we are going to do that, and this is just kind of part of it."
Webster said that his team will evaluate both Mariota and Winston during the NFL Scouting Combine, which starts this weekend in Indianapolis.
Mettenberger was selected in the sixth round of the 2014 NFL draft and started six times last season, losing each one of those starts.
He completed 60 percent of his passes for 1,412 yards with eight touchdowns and seven interceptions last season. He missed the last three games after injuring his shoulder.
"Zach has done a great job of everything we've asked," Webster said. "He's working hard, and it is important to him. He just needs to keep doing that. ... I know with all the questions it's difficult, but he just needs to keep doing what he is doing, and he understands that.
- Scooby Axson