The Vikings coaching search started to heat up Monday as team officials conducted another interview and arranged several more for later this week.

Led by General Manager Rick Spielman, the Vikings were scheduled to interview Arizona Cardinals defensive coordinator Todd Bowles on Monday and Cleveland Browns defensive coordinator Ray Horton on Tuesday. John Wooten, chairman of the Fritz Pollard Alliance, confirmed that both interviews were scheduled to take place in Phoenix.

The Vikings reportedly kicked off their interviews by meeting with Seattle Seahawks coordinators Darrell Bevell and Dan Quinn over the weekend.

On Monday, the Vikings requested permission to interview Cincinnati Bengals offensive coordinator Jay Gruden, according to a league source. The team also requested an interview with San Diego Chargers offensive coordinator Ken Whisenhunt, according to CBSSports.com.

The Vikings also are expected to interview Bengals defensive coordinator Mike Zimmer this week and possibly San Francisco 49ers offensive coordinator Greg Roman, according to reports.

Per league rules, the Vikings were not allowed to interview Gruden, Zimmer, Roman or Whisenhunt last week because their teams played in wild-card playoff games. Assistants on playoff teams that had a first-round bye were allowed to interview last week through Sunday.

Gruden and Zimmer can be hired at any time now because the Bengals' season is over. Roman and Whisenhunt can interview this week, but they can't be hired until after their season concludes.

Spielman vowed to conduct a thorough coaching search after firing Leslie Frazier last week. His interview list includes both offensive and defensive coaches with different levels of experience. He noted at his news conference that he established a list of 13 categories in which he classifies potential candidates.

Whisenhunt served as head coach of the Arizona Cardinals from 2007-12 and led the Cardinals to the Super Bowl in 2008. Bowles took over as interim head coach of the Miami Dolphins for the final three games in 2011. Zimmer is a veteran defensive coordinator who has interviewed for several head coaching jobs the past two seasons.

The Washington Redskins, Detroit Lions, Tennessee Titans and Cleveland Browns also are looking for head coaches.

"We don't have 'A guy,' " Spielman said. "I think there's a lot of potential candidates out there. I don't think everybody needs to panic [and say], 'This team already hired a guy. This team already hired a guy. What are the Vikings doing?' We are going to go through our process and do our due diligence, and I think there is enough to potential candidates out there that we will be able to get the guy that we want."

Zimmer, Horton and Bowles all have experience with 3-4 defensive schemes. Spielman sounded intrigued last week by the prospect of having a new defensive scheme.

"It will be interesting when you talk to a lot of these coaches, whether it's a 3-4 or a 4-3, some teams run a 4-3 with a hybrid 3-4," he said. "There are so many different things going out there. I am very excited about the process, just to learn and to talk to a lot of different people to see their philosophies."