Barca announced on Tuesday that Barjuan would not remain in the role after missing out on promotion into the second-tier of Spanish football last season.
Sources have told ESPN that Marquez, as first reported by Relevo, will take over, with "just the contract left to be signed" before an official announcement.
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Marquez, 43, was one of the first signings of Joan Laporta's first spell as Barca president in 2003 and went on to win two Champions Leagues with the club.
Laporta and Marquez have maintained a good relationship ever since and the Barca chief first attempted to bring him back to Camp Nou last summer.
He had been earmarked to take over the Under-19 team, but a deal fell through at the last minute due to his presence on a list in the United States linking him to drug trafficking.
The sanctions imposed by the U.S. Treasury Department could have had a knock-on effect for Barca in terms of their commercial activity in the United States.
However, Marquez, who always maintained his innocence, was removed from the list last September, finally teeing up his return to Barca.
It will be his second coaching job in Spain following a fleeting spell working as the manager of Alcala de Madrid's U16 side.
Barca Atletic play in the third tier of Spanish football and act as the bridge between the youth academy and the first team.