Shurmur is now available to talk and sign with another team following the Vikings lost 38-7 in the NFC Championship Game on Sunday night. The team had planned on bringing him in for a second interview (or meet and greet) this week.
The expectation is that a deal with the Giants could be done by Tuesday, a source told ESPN's Jordan Raanan.
Shurmur opted not to get into specifics after Sunday's loss. He thought there was probably "another time and place for that."
He flew back to Minnesota with the team on Sunday night.
"We're going to get on the plane and go back [Monday], and we got the exit [interviews] for the players and move on from there," Shurmur said.
The Giants interviewed Shurmur on Jan. 6 while the Vikings were on their bye week. It became apparent last week that their focus was on Minnesota's offensive coordinator to become the 18th head coach in franchise history.
Shurmur, 52, has spent the past two years with the Vikings. He has worked magic with quarterbacks Sam Bradford and Case Keenum. He previously served as offensive coordinator for the Eagles under Chip Kelly after two years as head coach of the Cleveland Browns.
Keenum had a rough game on Sunday -- one touchdown pass and three turnovers -- but had a career year working with Shurmur. He threw 22 touchdown passes and seven interceptions in the regular season.
Shurmur would replace Ben McAdoo, who was fired back in early December during the Giants' 3-13 season. He is expected to target former Oakland Raiders coach Jack Del Rio as his defensive coordinator, according to ESPN's Chris Mortensen.
When asked about his potential staff after Sunday's loss, Shurmur said he "wouldn't have any way to comment on that."
Shurmur has a strong history of working with and developing quarterbacks, even before joining the Vikings. The Giants and new general manager Dave Gettleman have the No. 2 pick in this year's draft, and they could be in the market for a quarterback, with Eli Manning turning 37 earlier this month.
With Gettleman and Shurmur, the Giants are believed to want to keep Manning for at least one more season.
Shurmur was one of six candidates who interviewed for the Giants job. New England Patriots offensive coordinator Josh McDaniels and defensive coordinator Matt Patricia, Carolina Panthers defensive coordinator Steve Wilks, interim Giants coach and defensive coordinator Steve Spagnuolo and former Denver Broncos running backs coach Eric Studesville were also interviewed.
The focus on Shurmur became apparent when it was reported last Sunday that Patricia would be the next coach of the Lions.