Wednesday have lost only one of their last 11 league games since former Northampton boss Gray, 52, joined Owls manager Dave Jones's backroom staff in mid-December.
Both Jones and Owls chairman Milan Mandaric told a Wednesday fans' forum that Gray was an integral part of the club's coaching team and wanted him to continue beyond the current campaign.
Jones said: "Stuart is happy in what he is doing. He's a very good coach.
"You don't just build a team on the field, it's important to build one off it.
"He came probably at the right time. He brought experience and a different approach.
"I'm sure if he still enjoys it, at the end of the season we'll be sitting down and speaking to him. He's helped us along."
Mandaric added: "Our manager will have support to keep Stuart. He is a tremendous addition."
Wednesday are unbeaten in their last seven league matches and sit five points clear of the relegation zone.