"I'm going to shower across the street, make sure my change of clothes are around the corner," Stoudemire said in an interview with Israeli website Walla Sport. "And I'm going to drive -- take a different route to the gym."
Asked if he was joking, Stoudemire responded, "I mean, there's always a truth within a joke."
Stoudemire is playing for Hapoel Jerusalem in the Israeli Premier League. Some teammates interviewed for the piece said they "wouldn't have an issue" with a gay teammate.
While he was playing for the Knicks, Stoudemire was fined $50,000 after he tweeted a gay slur at another user during the 2012 offseason.
At the time of the fine, Stoudemire issued an apology through a statement.
"I am a huge supporter of civil rights for all people," he said. "I am disappointed in myself for my statement to a fan. I should have known better and there is no excuse."
Information from The Associated Press contributed to this report.