Off contract from Manchester United, Lindelof is currently a free agent.
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While Bayer are in talks to sign Sevilla defender Loic Bade, Sky Deutschland says they have also made a contract offer to Lindelof.
The Sweden captain worked with new Bayer coach Erik ten Hag at United and the pair are keen on a reunion.
Bayer have offered Lindelof a 12-month deal with an option for another year.