TMW says the Seagulls are listening to offers for the Paraguay international and have already fielded enquiries from Real Betis.
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Enciso is this season on-loan with Ipswich Town and Brighton intend to cash in over the summer.
Brighton will listen to offers starting at €15m, though Betis would prefer a loan-to-buy arrangement for next season.
Betis coach Manuel Pellegrini is convinced by Enciso's potential and sees him as an ideal foil for Chucho Hernandez in his attack for next season.