Shurmur helped lead the Vikings to the NFL North title with a 13-3 record, doing so by getting an unprecedented performance from journeyman quarterback Case Keenum, who stepped in for injured Sam Bradford.
Keenum, an undrafted free agent in 2012, has completed 67.6 percent of his passes for 3,547 yards with 22 touchdowns and seven interceptions this season. His 98.3 passer rating ranked seventh in the NFL.
That helped raise the stock of the 52-year-old Shurmur, who has spent 30 years as a coach, including the last 19 in the NFL.
Shurmur is the third candidate to meet with the Bears. General manager Ryan Pace interviewed Chicago defensive coordinator Vic Fangio on Wednesday and Vikings defensive coordinator George Edwards on Thursday.
The Bears are looking to replace John Fox, who was fired after he went 5-11 in his third season as head coach.
Shurmur started his NFL coaching career with the Philadelphia Eagles in 1999, working as the tight ends and offensive line coach until becoming the quarterbacks coach from 2002-08. He was the Los Angeles Rams offensive coordinator for two seasons before his only head coaching assignment, with the Cleveland Browns in 2011 and 2012.
He was 9-23 in two seasons in Cleveland.
Shurmur went back to the Eagles as offensive coordinator from 2013-15. He joined the Vikings as tight ends coach in 2016, taking over the offensive coordinator role for the final nine games.