The Giants requested permission to speak with Garrett about their head-coaching position before hiring Joe Judge. They needed permission because Garrett was still under contract.
Garrett's contract with the Cowboys expired Tuesday, and the Giants brought him in to talk about being one of Judge's top assistants.
The Giants also interviewed Mike Shula for the job earlier this week, and Judge was expected to talk with former Cleveland Browns head coach Freddie Kitchens about a spot on his offensive staff. Shula was the Giants' offensive coordinator under Pat Shurmur and helped with the development of rookie quarterback Daniel Jones. Kitchens worked with Judge earlier in their careers at Mississippi State.
Garrett, 53, spent the past nine seasons as the Cowboys' head coach. He previously served as Dallas' offensive coordinator.
Garrett also has ties to the Giants organization, having played there from 2000 to 2003, and he is well-respected inside their building.
At Judge's introductory news conference, co-owner John Mara was asked about the possibility of hiring Garrett as the Giants' offensive coordinator.
"I certainly wouldn't have any objection to that," Mara said. "I have a lot of respect for Jason. At the end of the day, that's going to be Joe's decision."
Garrett's experience as a head coach could serve as an asset to Judge, who has never been a head coach at any level. Judge spent the past eight seasons as an assistant under Bill Belichick in New England, most recently as the special-teams coordinator and wide receivers coach.
Garrett had been with the Cowboys since 2007. He led Dallas to an 85-67 record as the head coach, making it to the playoffs three times.
The Cowboys finished 8-8 this past season and allowed Garrett's contract to lapse while hiring Mike McCarthy as his replacement.
Garrett has experience working with young quarterbacks. He was a key figure in the development of current Cowboys starter Dak Prescott, a fourth-round pick in 2016. Prescott finished fourth in the NFL with a QBR of 70.1 this season.
Jones, the No. 6 draft pick out of Duke last year, had his ups and downs throughout his rookie season. He threw 24 touchdown passes and 12 interceptions and also lost 11 fumbles.
Raanan: Giants respect Jason Garrett
Jordan Raanan breaks down the Giants' interest in hiring former Cowboys head coach Jason Garrett as their offensive coordinator.