The 19-year-old had been frozen out at Hillsborough in a long-running contract dispute, and only made his first Owls appearance - at any level - scoring for the Under-23s at Leeds United last month.
That return, and resumption of contract talks between the club and player, suggested Hirst could follow fellow youngsters Jordan Thorniley, Sean Clare and Jack Stobbs in being drafted into Luhukay’s first-team squad.
But, despite the relegation-threatened Owls in desperate need of goals - and strikers Gary Hooper, Steven Fletcher and Fernando Forestieri all out injured - Wednesday are refusing to allow Hirst to be considered for the senior team.
The striker’s contract is due to expire in the summer, with Premier League clubs like Leicester City and Everton - and Yorkshire rivals Leeds United - monitoring his situation.
"There is a different situation and everyone knows that," Luhukay said when asked of Hirst's availability at Thursday’s press conference.
"So I cannot answer that. In this moment yes [he is not available].
"We are not now speaking about the football. We are speaking about the personal situation between him and the club.
"I stay outside that. I cannot change the situation."
Hirst started Thursday’s Under-23 game with Crewe at Middlewood Road, which also saw a return from injury for midfielder Sam Hutchinson and defender Joost van Aken.
Keiren Westwood, the Owls goalkeeper who has not played for three months due to injury, has been called up by the Republic of Ireland for this month’s friendly with Turkey.