As speculation about his job security looms over the final week of the season, Vikings coach Leslie Frazier said Monday that neither he nor his agent has had discussions with ownership or general manager Rick Spielman about his status.

Several national reports have indicated that the Vikings already have begun contacting potential replacements. Frazier is signed through the 2014 season, but it’s unlikely the organization would want him to coach in a contract year because of the potential disruptions that would cause.

Frazier, who has a 20-33-1 record since taking over during the 2010 season, has faced questions about his job status multiple times the past few weeks. He’s handled the sensitive subject with poise and class, saying he’s only focused on helping his team prepare for the next game.

“I think for our players, it’s important that they focus on the task,” he said Monday. “That’s what I’m asking them to do, and I need to do the same thing. It’s very, very important if you want to have a chance to win these games down the stretch that I stay focused on what’s involved with leading our team and I want them to follow. It’s important I handle it the right way.”

Frazier’s fate already might have been determined privately by ownership, but a lackluster 42-14 loss to the Cincinnati Bengals on Sunday had an air of finality to it. Players and coaches looked and sounded emotionally exhausted as they neared the end of a difficult season.

Afterward, Adrian Peterson voiced support for Frazier and said he intends to talk to owners Zygi and Mark Wilf after Sunday’s finale against Detroit.

“I’m definitely not an individual that’s looking for dramatic change like that,” Peterson said. “It will hurt if he leaves.”

Peterson also tried to deflect criticism from Frazier and the coaching staff for Sunday’s dismal performance.

“It just seemed like we were in a funk,” he said. “Everything falls back on the players. We were prepared. Coaches did a great job of putting the things we needed to see in front of us to be ready to go out and execute.

‘‘Just as a group, we just didn’t do that. That falls back on the players.”

Asked about Peterson’s public show of support, Frazier seemed appreciative and then tried to steer the conversation away from his job status and focus on Peterson’s willingness to continue to play despite being injured.

“He’s a special player, special guy,” Frazier said. “We always want to just do the right thing by him when it comes to playing the game of football. He means so much to our franchise and our organization so you’ve just got to be wise when we’re talking about how to use him.”

The Vikings opponent in the season — and Metrodome — finale also appears likely to make a coaching change after the season. Detroit’s Jim Schwartz is firmly on the hot seat after a late-season meltdown eliminated his team from playoff contention.

The Lions were 6-3 at one point and appeared in good shape as the Green Bay Packers and Chicago Bears dealt with quarterback injuries. But Detroit has lost five of six games, including a 23-20 loss to the New York Giants in overtime on Sunday.

The Lions lost back-to-back home games to squander their shot at winning the division title. Schwartz evaded questions about his job status after Sunday’s loss.

“This is the truth: Speculation is not my business,” Schwartz said, according to the Detroit Free Press. “My business is coaching the team and trying to keep the team focused and I think that’s job enough without worrying about all the other stuff.

‘‘Where we were, we can’t worry about where we were. It’s where you are in the present and we came up short. We make no excuses for it.”