Mayuka joined 4th placed Metz this season from Southampton.
This is after the striker was omitted from the Metz team for Monday nights 1-0 home Ligue 2 win over Sochaux.
Media reports from France suggest that Hinschberger, who took charge in December, is planning to offload a total of six to seven players either out on loan or permanently in the winter transfer window.
Already, Turkish defender Sezer Özmen has left while strikers Juan Manuel Falcon and Amido Baldé are edging towards January exits with four slots left.
Mayuka, who has scored two Ligue 2 goals, was left out of the match against Sochaux together with fellow strikers Juan Kaprof, Moumhamadou Diallo and Celestin Djim who have all yet to score this season.
Abdoul Kaboré, who scored the games goal, was the lone striker selected for the fixture.