The 28-year-old has attracted interest from top clubs around Europe after impressing at this summer's World Cup for Norway, particularly for his performance against Brazil's Vinícius Jr in the 2-1 victory in the round of 16.
Dortmund will not consider any offers under €30M, per Germany's Bild.
United boss Michael Carrick is looking to strengthen his squad further ahead of the new Premier League season and a return to the UEFA Champions League, and it is thought that Ryerson can add quality in the full-back department.
Ryerson made 31 appearances for Dortmund last season, providing an impressive 15 assists.
His contract is valid until the summer of 2028, and it is unlikely that any potential deal will be agreed until after this summer's World Cup.