The two candidates are believed to be the first to interview with the Bears in person, according to the Chicago Tribune. Newly-hired consultant Ernie Accorsi, chairman George McCaskey and president Ted Phillips conducted the two interviews.
Gaine, 41, recently completed his first season with the Texans. Previously, he held high-ranking positions in the scouting departments of the Miami Dolphins, Dallas Cowboys and New York Jets, working with Bill Parcells at all three.
Dawson, 43, has spent the last eight seasons with the Titans. Tennessee has just one winning season in that period and has went 38-58.
The Bears are also expected to interview Kansas City Chiefs director of player personnel Chris Ballard on Wednesday. Ballard was a scout for the Bears for 11 seasons before spending the 2012 season as their director of pro scouting.
The Bears fired general manager Phil Emery along with head coach Marc Trestman last month. Chicago finished 5-11, last in the NFC North and missed the playoffs for the fourth straight season. Emery held the GM role for three seasons, over which the Bears went 23-25 and declined in every season after going 10-6 in 2012.
- Mike Fiammetta