Bevell flew to Seattle on Tuesday for a two-day interview with head coach Pete Carroll. After the interview, he was offered the job and contract talks have started. The source said the negotiations should be concluded within the next day.
Bevell was Minnesota's offensive coordinator for the past five years.
New Vikings coach Leslie Frazier hired Falcons quarterbacks coach Bill Musgrave to run the offense Wednesday.
John Clayton is a senior NFL writer for ESPN.com.