BBC Sport says BlueCo, which own both Chelsea and Strasbourg, are in advanced talks to sign Enciso.
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Enciso will move to Ligue 1 Strasbourg for €20m for this season with the long-term aim of eventually joining Chelsea.
The Paraguay international spent the second half of last season on loan at Ipswich Town.
Enciso was left out of Brighton's squad for the opening Premier League draw against Fulham last weekend.
Chelsea have sent goalkeeper Mike Penders, Kendry Paez and Mamadou Sarr all on loan to Strasbourg for the new season.