The 34-year-old is on loan with the Championship side until January and earned the man-of-the-match award for his debut display in the 0-0 draw with Watford.
Beye told BBC Radio Sheffield: "I think I will be here all season because I don't want to go back to Villa.
"Unless Doncaster kick me out, I will be here all season. It's a great club and I want to be part of it."
The Senegal international is happy to drop down a division despite Doncaster's precarious position.
"There's quality in the team and I don't think it is in the right place because if you look at it Watford are not in the bottom three and we are better than them," he added.
"At the end of the day we are in the bottom three and we have to work to get out."