The 26-year-old was on the books at La Masia for seven seasons from 2007 to 2014, but he left Catalonia without breaking into the Barcelona first team, subsequently joining Dinamo Zagreb.
After rising to prominence in Croatia, Olmo was the subject of a €29m (£24.6m) switch to Leipzig midway through the 2019-20 campaign, and he has continued to go from strength to strength for both club and country.
From 148 appearances in a Leipzig jersey, Olmo has registered 29 goals and 34 assists, and he was a cornerstone of Spain's Euro 2024-winning team in Germany this summer, despite initially being on the fringes of Luis de la Fuente's squad.
Olmo ended the tournament with three goals and two assists to his name, starting the semi-final win over France and playing the full 90 in the final victory over England following an injury to the luckless Pedri.
Leipzig 'to reject' £55.2m Barca bid
Olmo had already been attracting serious interest from top European clubs before lighting up stadiums across Germany, with Premier League titans Chelsea, Liverpool and Manchester City all linked with an approach.
However, Olmo is believed to favour a return to his erstwhile stomping ground, as it has been reported that the 26-year-old has reached an agreement over a six-year contract with Hansi Flick's team.
All that is left now is for Barca and Leipzig to agree on a fee, but the Blaugrana are yet to meet Die Roten Bullen's price demands, as Sport claims that they will soon have a second offer rejected.
Barcelona's latest bid is thought to be an upfront €50m (£42.5m) with up to €15m (£12.7m) in performance-related add-ons, but Leipzig want a guaranteed €55m (£46.7m) to let Olmo leave.
In addition, Barcelona's payment structure is thought to represent the biggest roadblock to an agreement, as the Blaugrana hope to fork out the fee in small instalments amid their long-running financial issues.
While Leipzig wish for the upfront €50m (£42.5m) fee to arrive in full within a few months, Barcelona may have to postpone part of that payment for a year or more.
The Spaniard's Leipzig contract formerly contained a release clause worth €60m (£51m), but that option expired in the middle of January, meaning that his current club hold all the cards at the negotiating table.
Nevertheless, Barcelona are supposedly still confident that they can find a breakthrough with their German counterparts in the coming days, as Olmo is determined to seal a return to Camp Nou.
What about Barcelona's pursuit of Nico Williams?
Olmo is just one of two triumphant Euro 2024 attackers whom Barcelona are determined to sign this summer, as the La Liga giants have long been considered the favourites for Athletic Bilbao's Nico Williams.
However, the report adds that a deal to bring the 22-year-old to Camp Nou is currently highly unlikely, hence Barca's push to sign Olmo, but they are not giving up hope of luring Williams to Catalonia too.