Gunners and United free to move for midfielder.
The German international has been linked with a number of top clubs throughout his career, having long been regarded as one of the best young players in Europe.
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Arsenal transfer news
A slight dip in form has seen him remain with Schalke, but it has been rumoured that Wolfsburg could move for him to replace departing star Kevin De Bruyne, who was confirmed as a new Manchester City player on Sunday.
However, the Daily Star reports that Schalke have denied this speculation, meaning there could still be a chance for either Arsenal or United to pull off a late move for the 21-year-old.