Ole Gunnar Solskjaer was unable to sign a midfielder before the Premier League's transfer window closed on Thursday.
However, he did attempt to secure the services of Olmo, who starred in Spain's victory at the European Under-21 Championship in June.
United offered £24m for the former Barcelona youth-teamer, but their bid was immediately rejected by Dinamo.
United begin the 2019/20 campaign against Chelsea on Sunday.
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