Speaking with Germany's Sportbild magazine in an interview published Wednesday, Ballack reflected on his experience with Kaiserslautern in 1997-98, who won the Bundesliga title the year they were promoted to the top division.
"Dreaming is allowed. Why not?" said Ballack, who played for Kaiserlautern before joining Bayern and later moving to Bayer Leverkusen and Chelsea.
"I experienced that with Kaiserslautern in 1998 when we became champions after being promoted.
"Or there is the example of Leicester, who surprisingly won the Premier League title in 2016."
Union are top of the Bundesliga after seven matches and are the league's only unbeaten team.
In just their fourth season in the top division, Union have taken 17 of a possible 21 points so far this season, including a 1-1 draw against Bayern Munich.
Union finished 11th in their first season in the top grade and followed that with seventh and then fifth-placed finishes.