The Giants are planning to schedule a second interview next week with Shurmur, sources told ESPN's Dan Graziano and Chris Mortensen. They are intent on strictly adhering to NFL rules that prohibit contact with the candidate, negotiation with an agent or any agreement after the initial interview window closed.
Teams are permitted to have second interviews with candidates who are coaching teams in the Super Bowl beginning next Monday. The Vikings are playing on the road Sunday against the Philadelphia Eagles in the NFC Championship Game.
If Minnesota loses, the Giants can negotiate or sign Shurmur immediately.
Vikings coach Mike Zimmer expects to lose Shurmur, sources told Mortensen. Shurmur is also a candidate for the Arizona Cardinals job.
A source told ESPN on Monday afternoon that Shurmur wants the Giants job.
Shurmur has a strong history of working with and developing quarterbacks. 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.
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 began when Patricia, believed to be a favorite of the Giants, was reported by ESPN's Adam Schefter on Sunday to be the next coach of the Detroit Lions.
Shurmur, 52, was a longtime assistant with the Eagles under Andy Reid before becoming the offensive coordinator for the Rams under Spagnuolo. He then was the head coach of the Cleveland Browns for two seasons, when he amassed a 9-23 mark. He later returned to Philadelphia as Chip Kelly's offensive coordinator before landing with the Vikings.
After the Ben McAdoo era crashed in its second season, the Giants are looking for a coach who has either been a head coach or had significant experience as a coordinator. Shurmur has both.
One source who worked with Shurmur called him a "really smart offensive coach" whose players love playing for him. His track record of success in recent years with quarterbacks is among his most impressive accomplishments. Shurmur has gotten career years out of Nick Foles, Sam Bradford and, most recently, Case Keenum.
Keenum threw 22 touchdown passes and seven interceptions this season working with Shurmur. Minnesota finished 11th in total offense this season.