Mandaric has said that while he will give Gray the time to impress, he will not stop looking for a new permanent manager.
"[Gray] has shown signs of turning things around," Mandaric told the Irish Independent. "I think he deserves a chance before we start to be more aggressive to bring people in.
"We have not stopped [looking for a manager] completely, but we are not pushing for anyone. I am trying to allow time to see what Stuart can do. If we need to go for a new manager, that will happen soon.
"But in the meantime I would like to give Stuart a chance. It is up to him. I am not keeping my head in the sand and ignoring the situation where we are, but right now, Stuart is the way we need to go."
Former Aston Villa manager Alex McLeish is the bookmakers' favourite to succeed Jones at Hillsborough.