Bayer general manager Wolfgang Holzhauser has told the former Chelsea man time is running out for him to decide whether he will rejoin his old club.
Holzhauser said: "By the start of training on Monday we want clarity."
Ballack, 33, is a free agent after Double winners Chelsea decided against offering him a new deal.
He is being chased by a number of clubs but, unlike Holzhauser, Bayer sporting director Rudi Voller insists the midfielder will not be rushed into a decision.
He said: "We a battling for Michael's services. We have good arguments on our side and I hope he opts for us.
"We will not put Michael under pressure. It certainly does not depend on one or two days."