Gray, who finished third in American League Cy Young voting last year, has endured a rocky encore, pitching to a 5.74 ERA across 21 starts in a season that's included two disabled list stints.
The A's would like to see him return to form again this year but not at the expense of his health, particularly given their place in the standings with just seven weeks of play remaining. Gray hasn't pitched since Aug. 6.
Melvin said Sunday he was unsure whether Gray would make another start in 2016.
"It just depends," he said. "I don't know that it's necessarily important, but it's nice to know that you're healthy again and you don't have to worry about it in the offseason. But it's not like we're going to push him to try to get him out there just to get him out there."
The A's have been fielding a patchwork rotation of late but could gain some stability soon in Jesse Hahn. Melvin said the right-hander is set for a rehab start with Triple-A Nashville on Tuesday, putting him on track for a Sunday return against the host Chicago White Sox.
Jane Lee is a reporter for MLB.com. Follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.