Downing is expected to be hired as an offensive assistant to help with the passing game, ESPN reported Saturday.
Downing, who spent one year leading the Raiders' offense, was fired after the season when Jon Gruden was hired as head coach.
Downing, a Minnesota native, would work with John DeFilippo, hired earlier to replace Pat Shurmur as Vikings offensive coordinator. Shurmur left Minnesota on Jan. 22 to become head coach of the New York Giants
The 37-year-old Downing was on the Vikings' staff from 2001-2005. His last job with Minnesota was as a quality control coach. He also served as a quarterbacks coach with the Buffalo Bills, Detroit Lions and Raiders.