Gay will become a restricted free agent in July.
"Rudy is our No. 1 priority," general manager Chris Wallace said. "Our intent is to keep Rudy in a Grizzlies uniform."
Gay plans to use the team's direction as an issue during negotiations.
"This has to progress in the right direction. I love being here, but I'm at the point where I want to win," Gay said. "I want to have an understanding that we're trying to get into the playoffs. How much of an effort are we making? Memphis is a great city. It deserves a winning team, a playoff team. I'm going to do my best to achieve that if I'm here."
Gay turned down a five-year, $50 million deal before the start of this season.