According to Sky Sports, if he impresses, the Midland club is expected to move quickly to sign the former Chelsea and Atletico Madrid forward.
Wolves are in need of a striker following the ACL injury suffered by new signing Sasa Kalajdzic over the weekend.
Kalajdzic only arrived this summer from Stuttgart in a £15.5m deal plus add-ons.
It was a double blow for Wolves on Saturday, with Lage losing striker Raul Jimenez to injury in the warm-up.
Costa is a free agent and Bruno Lage’s side can sign him outside the transfer window.