With the Cowboys 21-17 upset loss to the New York Giants in the NFC divisional round, there are no longer any NFL rules stopping the Ravens from hiring Garrett, who is widely considered the front-runner for the Ravens job.
If the Ravens don't immediately pursue Garrett, it could mean they covet someone else.
Garrett is one of six NFL assistants who have interviewed with the Ravens since the team fired Brian Billick on Dec. 31.
Team officials have refused to comment on the specifics of their search, but there has been speculation that owner Steve Bisciotti favors Garrett.
It doesn't appear that Dallas will stand in the Ravens' way if they want Garrett.
After the Cowboys' playoff flop, owner Jerry Jones reiterated he would stay with coach Wade Phillips and said he was prepared to lose assistants to head coaching positions.
"I can't elaborate on [Garrett and assistant head coach Tony Sparano], but certainly part of my job is to make sure that, on a timely basis, we're able to address what happens to our staff," Jones told Dallas reporters. "When you enjoy success, you're going to lose coaches. I should and do have prospective coaches I would think of if we have openings."
Garrett declined to talk about his future except to say he would be at the Cowboys' season-ending meetings today.
If the Ravens don't hire Garrett or another young assistant, the Ravens might turn to veteran coach Marty Schottenheimer, who has been contacted by the Ravens but has not interviewed with team officials.
The Ravens have not interviewed a candidate for the past five days.
Other teams could wrap up their coaching hunts this week, too.
The Miami Dolphins are expected to hire Dallas assistant head coach Tony Sparano, and the Atlanta Falcons seem ready to name a coach after hiring Tom Dimitroff to be their general manager.
It is believed that former Ravens defensive coordinator Rex Ryan is a strong candidate for the Falcons job.