The Major League Soccer club want the 43-year-old to replace Chris Armas, who was sacked earlier this month.
Talks are ongoing between all parties, but reports in Struber's native Austria say a deal is virtually agreed.
He took charge of Barnsley in November 2019 and succeeded in keeping them in the Championship with victories in their final two games.
Last week Barnsley chief executive Dane Murphy confirmed there was a "buyout clause" in Struber's contract.
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