While admitting that the Owls are "fighting" with other clubs in the transfer market, Gray is confident that more signings are on their way.
"We aren't far away," he told The Star. "The thing is we are fighting against other clubs who are in for these type of players. It's down to the agents and clubs agreeing the deals.
"We need to do more business. "We are still trying to strengthen the team. We need that little bit of quality. I want players to be pushed."
Wednesday get their Championship campaign underway with a trip to Brighton & Hove Albion on August 9.