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Attacking midfielder Havertz is one of the most sought-after players in world football and has been tipped for a big-money move in the next transfer window.
Premier League giants United and Bundesliga champions Bayern are said to be favourites for his signature, though Leverkusen director of sport Rudi Voller said this week the club hope to keep him for one more season.
Germany legend and former Leverkusen midfielder Ballack believes it is imperative the BayArena side finish in the Champions League places to do so.
"I think he's a great talent. He has outstanding technical skills and plays very freely," Ballack told Sport 1.
"It will be important for him to always play in the Champions League in order to be able to compete with the best. Therefore it will be important for Leverkusen to reach fourth place."
Havertz has stood out in the Bundesliga this season, contributing 11 goals and five assists to Leverkusen's cause.
However, Ballack warned the 20-year-old still has plenty of room for improvement.
He added: "One thing is clear - Havertz is not yet a finished player.
"That is not meant negatively, but I still see potential for improvement in his personality development and body language.
"But that is completely normal at his age. As a captain, he first has to learn to deal with this responsibility.
"His style of play has always been very carefree. If he ever lost the ball, he was allowed to stop. With a top club, everything will be more difficult and will no longer be accepted.
"He must and will be aware that he has an exceptional position in Leverkusen. He should ask himself now, 'How long do I want to have this? How long do I enjoy it? Or will I take on the next challenge with even greater demands on my game this summer?'.
"It comes with games and experience, especially with your own aspirations. It is crucial what Havertz demands from himself and his team and where his own path should lead.
"In any case, he has to be mentally ready for a change."