Olmo, who helped Spain to the Euro Under-21 Championship, began his career in the Barca academy.
But now reports in Croatia suggest United have bid £36m for the Dinamo Zagreb star.
Real Madrid and Bayer Leverkusen have also been linked to the 21-year-old attacking midfielder.
In other news, Barcelona midfielder Denis Suarez has agreed to move back to his boyhood club Celta Vigo.
“Barcelona and Celta Vigo have reached an agreement for the transfer of Denis Suarez. The Galician club will pay Barcelona 12.9 million euros (£11.6m) in variables,” Barca announced in a statement.
“Barcelona would like to publicly express its gratitude to Denis Suarez for his commitment and dedication and wish him every bit of luck and success in the future.”
Spaniard Suarez, 25, came through Celta’s academy and played for the reserves before moving to Manchester City aged 17 but he never played a competitive game for the Premier League side.