The 21-year-old spent seven years in the Barca youth system between 2007 and 2014 before leaving for Dinamo having failed to make the breakthrough at Camp Nou.
Olmo has been in impressive form for his Croatian club this season, scoring eight times and contributing seven assists in 22 appearances in all competitions.
A number of clubs, including Real Madrid and Atletico Madrid, have been linked with the Spain international, but according to Mundo Deportivo, Barca have made an offer to bring the attacker back to Camp Nou.
The report claims that Dinamo are expected to reject the opening bid, although the Catalan giants are confident that they will ultimately be able to complete a deal either in January or at the end of the campaign.
Olmo, who scored on his Spain debut in November, has managed 34 goals and 28 assists in 124 appearances for his current club in all competitions.