City manager Pep Guardiola confirmed last week that Garcia has turned down an offer to extend his contract with the club.
The 19-year-old will thus be available on a free transfer when his deal at the Etihad Stadium expires next summer, and he could sign a pre-contract agreement in January to cement a switch to Barcelona or another side.
But Barcelona reportedly want to sign Garcia for the 2020-21 season and are keen to sell Samuel Umtiti and Jean-Clair Todibo in order to make space in the squad and ease the financial hit of the center-back's potential arrival.
The coronavirus pandemic has taken a toll on Barcelona's transfer budget. As a result, they will only spend the funds they raise in outgoing transfers, Llorens and Marsden report.
Garcia was on Barcelona's books before he moved to Manchester City in 2017. He was a regular alongside Aymeric Laporte in the heart of City's defense following the restart of English football in mid-June, but Fernandinho replaced him for last week's Champions League elimination of Real Madrid.