Belgrade's private Beta news agency said Kovacevic signed the contract to play for KK Vrbas, a local basketball club that plays in a regional Serbian league.
"The club today signed a contract with Kovacevic, and he's now our registered player," the Vrbas captain, Bojan Markovic, was quoted as saying by Beta.
The team "is on his side," Markovic said, adding that he expects that Kovacevic shows up for the start of the club's practice sessions on Aug. 10.
Kovacevic's refusal to return to the U.S. to face charges has touched off a diplomatic crisis between Serbia and U.S. officials demanding his return.
Serbian law does not allow him to be extradited, and Serb officials have suggested U.S. authorities should hand over the full case file so they can consider whether Kovacevic should be prosecuted in Serbia.
Steinhauer, 22, remains in critical condition.