The 29-year-old Schultz has scored one goal and two assists in 62 games for the Wild this season.
He has two years remaining on the six-year deal he signed with the Wild in 2008 with an average annual value of $3.5 million.
Schultz was originally selected by the Wild in the second round (33rd overall) of the 2002 NHL Entry Draft.
Gilbert, 29, has scored three goals and 14 assists in 47 games for the Oilers this season.
Originally taken in the fourth round (129th overall) at the 2002 NHL Entry Draft by the Colorado Avalanche, Gilbert has scored 33 goals and 125 assists in 384 career games with the Oilers.
Two years remain on the six-year deal Gilbert signed with Edmonton in 2008 worth an average annual value of $4 million.