He's also not limiting what he wants in the Titans' next coach.
''The biggest thing to me that you can't do is rule out guys,'' Webster said. ''`I want an offensive guy or a defensive guy, previous head coaching experience.' . It causes you to miss out on possibly some good candidates.''
Webster wants to start interviewing candidates as soon as possible to replace Mike Munchak, who was fired Saturday after three years as head coach and 31 seasons with the franchise overall.
The general manager says some of the candidates he wants to interview still are coaching in the playoffs. With the Titans firing Munchak six days after the regular season ended, they missed the window to interview candidates whose teams had a bye this week.
The last time the Titans went looking for a new coach was late January 2011 after Jeff Fisher was fired with all other openings in the NFL already filled. Munchak was hired Feb. 7, 2011.
This time, the Titans became the seventh team in the league to fire a coach, but only the Texans and Buccaneers have hired replacements.
''We definitely have a head start on that,'' said Webster, who assisted then-general manager Mike Reinfeldt in 2011. ''I think we need to go through the process and make sure that we make the right decisions. So I can't really give you a timetable.''
Webster said he plans to meet with assistant coaches starting Monday. Munchak's firing happened so quickly after nearly a week of meetings that Webster said he hadn't completed the process yet with Titans president and chief executive officer Tommy Smith.
This franchise hired its last two coaches by promoting from within. Munchak had been offensive line coach when the Titans picked him in 2011, replacing Fisher, who took over for Jack Pardee after 10 games in 1994 for the then-Houston Oilers. Pardee was hired in 1990 away from the University of Houston.
Webster said he's watched people such as Rich McKay and others hire coaches when he was with the Buccaneers and Seahawks. Webster said he's not sure how many coaches were hired during his time in Tampa Bay, but it was a lot.
''I feel comfortable doing it,'' Webster said. ''I'm excited. I'm excited for the city. I'm excited for the Titans organization to move forward and find a coach who is going to be a good fit for Nashville and that they're going to be proud of, and we'll put a team on the field that they're proud of.''
ESPN.com reported Sunday that Seahawks defensive coordinator Dan Quinn is a leading candidate.
Quinn was assistant head coach in Seattle in 2009 when Webster was vice president of player personnel for the Seahawks. Other coaches being mentioned include Cowboys special teams coordinator Rich Bisaccia, Seattle offensive coordinator Darrell Bevell and Vanderbilt coach James Franklin.
Whoever Webster hires will need a plan to develop