The Spain international is on-loan at Chelsea this season from Atletico Madrid. However, his commitment to the deal has come into question after failing to secure a regular start under manager Thomas Tuchel.
El Chiringuito says Barca, where new coach Xavi has just been installed, is interested in Saul for January.
The Catalans could seek to take over Saul's loan from Chelsea over the New Year.
The stumbling block, though, could be Atleti's board, which may be reluctant to strengthen a direct rival midseason.
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