Ulloa tabled a transfer demand to Leicester this week.
Marca says Alaves have made a firm bid for the Argentine striker, seeking to buy Ulloa outright.
Ulloa would be happy to return to the LaLiga and join the Alaves project. After his experience at Castellón and Almería, the 30-year-old Argentine forward, who last season scored six decisive goals for Leicester to win the Premier League, would return to Spain after almost four years in English football.
Today, Ulloa is expected to demand Leicester sell him to Alaves in face-to-face talks.