The Cowboys interviewed receivers coach Ray Sherman to satisfy the NFL's "Rooney Rule," which requires teams to interview at least one minority candidate.
Cowboys owner Jerry Jones denied a move had been made, saying before Sunday's season finale against the Philadelphia Eagles that "nothing has changed from Monday regarding our coaching status at all."
But Jones may have tipped his hand after Sunday's 14-13 win against Philadelphia when he was asked if the new coach would have input into hiring the rest of the staff.
"That is certainly something that Jason needs to have input in," Jones said. "By the way, Jason had input in many of the staff members we have right now."
Jones denied having interviewed any candidates and Sherman also denied he had been interviewed, though Jones said he plans to interview Sherman.
"I'm really interested in following the spirit of the NFL rules and that's what this is all about," Jones said. "I just want to move on so that we can have the coaching decisions out of the way and move on and do what we need to do."
Garrett is surely the frontrunner. He went 5-3 since replacing Wade Phillips at midseason. Jones said he was very pleased with Garrett's performance over the second half of the season.
Jones says he won't require an interview with Garrett.
"I know him real well," he said.
He did predict "significant turnover" for a team that saw its Super Bowl hopes vanish after a 1-4 start. Jones refused to say the Cowboys would have turned the season around faster had he fired Phillips earlier in the season.
The Cowboys' three losses under Garrett have been by a total of seven points.
"We're not as good as I thought we were when we started," Jones said.
Garrett, a former NFL quarterback, joined the Cowboys in 2007 as offensive coordinator. He long was considered the coach-in-waiting in Dallas.
The Associated Press contributed to this report.