The newspaper says many reports have the team looking to move Gay in order to shed payroll and acquire a lottery pick in the upcoming draft.
"We're not looking to trade Rudy Gay," Heisley told the Commercial Appeal. "We're not shopping him around. Period. Do we sit around and say 'What if we traded Rudy, who could we get?' No. Right now, Rudy is part of the future of this team."
Gay will make $16.4 million next season, making him the team's second highest paid player behind only power forward Zach Randolph ($16.5 million).
Gay is owed about $53.6 million over the next three seasons after signing an $84 million contract as a restricted free agent in 2010.
After returning from shoulder surgery, Gay averaged 19 points and 6.4 rebounds for the regular season.
The Grizzlies were eliminated by the Los Angeles Clippers in seven games in the first round of the playoffs.