Schultz became one of the most sought-after unrestricted free agents on the market when he did not reach a deal with the Anaheim Ducks, the team that selected him in the second round of the 2008 NHL Draft.
The 21-year-old played the past three seasons at the University of Wisconsin, where he was a two-time finalist for the Hobey Baker Award.
"Are we interested? Of course we are," Oilers general manager Steve Tambellini said Wednesday. "We believe we present an incredible opportunity."
Earlier Wednesday, the Oilers promoted associate coach Ralph Krueger to head coach. The team selected forward Nail Yakupov with the No. 1 pick in last week's NHL Draft, adding him to a young core that includes Ryan Nugent-Hopkins, Taylor Hall and Jordan Eberle.