The USA international is the subject of transfer talks between Parma and BVB this week.
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However, Borussia Monchengladbach are now expressing interest and have made an offer for the midfielder.
For the moment, Dortmund are yet to respond, so leaving the door open to Parma to make a bid of their own, says Sky Deutschland.
Reyna is ready to leave Dortmund this month in an attempt to reignite his career after a difficult past two seasons.