The Scotsman may have caught the eye of interested parties during his performance against pre-season opponents Benfica in the Emirates Cup last week.
Burke has only been at the Bundesliga club for a season following his £15m switch from Nottingham Forest, but the 20-year-old winger struggled for first-team action.
The youngster made 25 league appearances in total, but in only five of them was he included in the starting lineup.
Ragnick told Bild: "I talked to Oliver once again in London and told him that we don't want to let him go. Against Benfica, he showed just how much he has in him. When he gets his pace into play, he can have an impact.
"It just doesn't make any sense for us [to loan him out]. He would go somewhere where he's not trained in the way we play."
Burke also scored one goal and created two assists in Germany's top flight last season.