Gray took charge of the first-team following the departure of manager Dave Jones this week and the struggling Owls claimed a 2-1 win over Leicester in his first game at the helm on Tuesday.
Chairman Milan Mandaric has confirmed that former Sheffield United manager Neil Warnock is among the candidates for the vacant job.
But Gray is also set to hold talks with Mandaric and will hope to strengthen his claims with another win at Hillsborough this weekend.
"He asked me again to take charge of the team for this Saturday's game against Forest," said Gray.
"I thought it might only have been the one game against Leicester, but like I say, a good result, a good performance, so I've probably bought him a bit of time to carry on his interviewing."
Gray believes the inclusion of Warnock on the shortlist shows that the club are attracting candidates with a decent track record in the Championship.
"Neil is very experienced, very knowledgeable. Had success at other football clubs and that's why this job is appealing to that sort of quality of applications of the job," he said.