The probe has been launched by the US Fish and Wildlife Service (FWS), BBC reported.
American dentist Walter Palmer killed Cecil the lion, the beloved big cat of Zimbabwe on July 1 in Hwange National Park.
The US Fish and Wildlife Service (FWS) said it was "deeply concerned" about the "tragic" death of Cecil the lion.
Director Dan Ashe said they will "go where facts lead" but efforts to reach Walter Palmer have been unsuccessful.
The clinic he runs in Minneapolis has been closed since he was named as the tourist who shot Cecil. Protesters carrying placards saying "Justice for Cecil", "Trophy hunters are cowards" and "Prosecute poachers" gathered outside the building on Wednesday.
On Thursday, the White House said it would review a public petition to extradite the American dentist after more than 100,000 signed it.
But spokesman Josh Earnest said it was up to the US justice department to respond to any extradition order.