Gray, 53, has been in charge of the Owls since Dave Jones was sacked at the start of the month and has a mixed record winning two, drawing two and losing two of his six games since taking over.
"We'll give Stuart another two games and see how he gets on," Mandaric said.
"He has done a pretty good job up to this point."
He added: "We have a lot of injuries and you have to give him credit for how he has done with the team.
"For now everyone needs to get behind him and the team because we want to do things the right way.
"If it's not going to be Stuart, then we need to make sure that the person who comes in can do better than him."
The Owls, who are two points from a position of safety in the Championship, host Blackpool on New Years Day before visiting Conference Premier side Macclesfield in the FA Cup on Saturday.