The Robins have said they want over £1m for Parkin if they are to sell him this summer.
Parkin has also been linked with a move to QPR in the past week, along with numerous other clubs.
His current deal has another year left to run, and the West Country side are still hopeful that he will sign an extension.
Director Sandy Gray said: "Sam has been an integral part of our club for three seasons now, scoring over 70 goals in the process. Why would we want to let him go?"