The forward suffered the knock in his side's 2-0 pre-season win over Chorley, where Grayson revealed that the 29-year-old "jarred his knee".
Grayson told the Evening Post: "Stuart has taken a knock and we'll see how he is over the next few days. It is not ideal that you get injuries in pre-season and hopefully it won't be too bad.
"He tried to ride the challenge but got caught and that jarred his knee."
Beavon joined Preston from Wycombe Wanderers in 2012.