The 37-year-old former Bulgaria midfielder retired from football in 2013 after being diagnosed with an acute form of leukaemia a year earlier.
Petrov was invited to Villa's pre-season training camp in Austria this summer with a view to making a return.
But he has been offered a different, unspecified role at the club.
Manager Roberto Di Matteo said: "Stiliyan is an inspiration to all of us. I have spoken to him and explained my thoughts and offered him the chance to remain at the club.
"Stiliyan is going to discuss this with his family before coming back to us."
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Former Aston Villa captain Stiliyan Petrov will not be offered a playing contract after returning to train with the club this summer.