Barcelona will come up with another offer for Eric Garcia that won't exceed €15m, Mundo Deportivo's Fernando Polo and Gabriel Sans understand.
Man City are said to consider bids worth €18m or more.
Barca's rumoured first offer of €10m was rejected by the Citizens.
In no case will Barca pay more than €20m for the centre-back, the source adds.
If City reject another bid, Barcelona will likely seal the deal for the 19-year-old in January, 6 months before his contract with Man City expires.
Eric Garcia was part of La Masia between 2008 and 2017.
Last season, the centre-back made 20 appearances for Pep Guardiola's side.
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