IRVING, Texas -- Jason Garrett will become a free agent of sorts, but he wants to continue as the head coach of the Dallas Cowboys.

Asked on 105.3 The Fan in Dallas if he wants to be the team's coach, Garrett said, "Absolutely."

"This is a great organization. I think we really built a football team that we can be proud of, and there are some really good things ahead for this team," he added.

The Dallas station also interviewed Cowboys owner/general manager Jerry Jones and executive vice president Stephen Jones later Monday. Stephen Jones said he started working on Garrett's new contract Sunday night and has continued in his work on it on Monday. Re-signing Garrett is the team's top priority, Jones said.

Jerry Jones, meanwhile, said Garrett was "my coach of the year" after Sunday's 26-21 loss to the Green Bay Packers and has continuously throughout the year said he wants Garrett to be the team's head coach for the long term.

Now the process starts on re-signing Garrett, who has a 42-32 career record, to a multiyear contract.

The bulk of the coaching staff is working on expiring contracts, including passing game coordinator Scott Linehan, defensive coordinator Rod Marinelli and offensive coordinator/offensive line coach Bill Callahan.

According to Pro Football Talk, Marinelli is expected to join the Tampa Bay Buccaneers, possibly as defensive coordinator, to reconnect with Lovie Smith, with whom he worked for the Chicago Bears from 2009 to 2012.

Garrett would not comment on the report but said the team wants to keep him.

"I know Rod Marinelli has done a fantastic job for us since he's been here," Garrett said. "He's done a great job coordinating our defense this year. We have every intention of keeping Rod Marinelli in his current role as defensive coordinator. We'll take care of the business things after we take care of the business of today, but Rod's a helluva coach and has done amazing things with our football team this year."

According to ESPN NFL Insider Adam Schefter, the Cleveland Browns have requested permission for offensive coordinator interviews with Callahan and Linehan.

A source told Schefter the Jacksonville Jaguars also requested permission to interview Callahan.

Jones blocked Callahan from interviewing with the Baltimore Ravens and Browns about their offensive coordinator vacancies last year despite giving his playcalling duties to Linehan.

The Cowboys hold three days of negotiating exclusivity with the assistant coaches before they are free to talk with other teams. During the exclusivity period, other teams have to request permission to speak to the Cowboys' assistants.