The 17-year-old forward has been in fine form for the academy side, notching up two goals in four games.
The Republic of Ireland youth international also bagged a goal on his debut in a pre-season friendly at Basingstoke in July.
Burns, assistant academy director, has been overseeing the under-18 side in Tony McAndrew's absence - with the youth manager assisting Kevin MacDonald in first team duties.
Burns has been very impressed with Burke's impact at the club.
He told Villa's website: "Graham is a very interesting footballer.
"He is very calm and very composed and technically very good.
"He is one of these players that seems to be able to find space and also calm things down when needed too. He is a goalscorer, no doubt. He also links play very well between the midfield and the strikers. His general all-round play is very good.
"He is only 17 so he has a little bit of growing to do. When he grows and gets more mature as a footballer, I am sure he will be a very effective player for us. He has a good start to the season. He has played in the reserves a couple of times and he's been a regular in our side too."