Manchester United submit bid for Spanish midfielder – report
Olmo starred at this summer's European Under-21 Championship, helping Spain win the tournament for a fifth time.
And the youngster's performances in Italy have brought him to the attention of a host of European clubs.
Chelsea, Liverpool, PSG, Inter, Bayern Munich and Borussia Dortmund are all keeping tabs on the playmaker.
However, United hope that their early offer will allow them to steal a march on their rivals.
Ole Gunnar Solskjaer wants to add more creativity to his squad after United missed out on the top four last term.