The 22-year-old has been in impressive form for his German club during the 2020-21 campaign, scoring five times and providing 11 assists in 40 appearances in all competitions.
Olmo has a contract at Leipzig until June 2024, but there is believed to be a €80m (£69m) release clause written into the deal.
According to Sport, Barca have already made contract with the attacker's representatives and are planning to launch an offer when this summer's transfer window opens for business.
The report claims that the Catalan giants are not prepared to meet the Spain international's release clause but are confident of agreeing a cut-price deal in the upcoming market.
Olmo has netted 10 times and provided 12 assists in 55 outings for his Bundesliga side since making the move from Dinamo Zagreb in January 2020. body check tags ::