According to reports in Croatia from Sportske Novosti, Ole Gunnar Solskjaer was keen on bringing the 21-year old to Old Trafford and the Red Devils failed in a deadline day bid for him.
Fellow Premier sides Everton and Wolves were also reported to be interested in a move, however nothing materialised in time before the window closed on August 8.
With the Premier League transfer window now closed until January 2020, United will have to shelve their interest in the former FC Barcelona youth team player.
The Croatian side do not want to sell Olmo, and are reported to be only potentially considering bids in the region of €40m for the talented play maker.
They are keen to tie him to a new long term contract, with his current deal set to expire in 2021, however Olmo's representatives have indicated that he is looking for a move away from Croatia.