Eriksen remains a free agent after leaving United over the past summer and is currently training with Malmo FF in Sweden.
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The Daily Express says an opportunity for Eriksen is emerging at Bayer after former Denmark coach Kasper Hjulmand was named new trainer on Monday.
Hjulmand takes charge after the dismissal of former United manager Erik ten Hag following just three games in charge.
Eriksen and Hjulmand are close following their time together with Denmark.