Marinelli's meeting with the Cowboys comes one day after new Bears coach Marc Trestman said Marinelli had decided to move on.
In Dallas, Marinelli would become the club's defensive line coach. He is being considered for the job because of his ties to new Cowboys defensive coordinator Monte Kiffin, who runs a Tampa 2-4-3 defensive scheme.
Marinelli spent four seasons with the Bears, including the past three as defensive coordinator. He was previously the defensive line/assistant head coach.
The Bears' defense ranked fifth in total defense this season, 17th last season and No. 9 in 2010. The Bears led the NFL with 24 interceptions, including eight for touchdowns, this season.
Marinelli was the Lions' head coach from 2006-08. He went 10-38, including an 0-16 record in 2008.
Information from ESPNChicago.com's Michael C. Wright was used in this report.