Alba was available for a possible Inter Miami debut in Leagues Cup match against Florida rivals Orlando City after arriving in Miami at the weekend. The 34-year-old won five Spanish league titles and a Champions League title during his time with Barca and a European Championship and Nations League with Spain.
"I have come here to compete, to win everything," Alba told a press conference after training on Tuesday.
Alba said the impact of Messi and Busquets, who led Miami to back-to-back wins over Cruz Azul and Atlanta in the group stage of the competition, has already been evident. "I think the arrival of Busi (Busquets) and Leo (Messi) has made the team grow a lot", Alba said. "And I'm going to be the same player I've been in Europe, I'm going to have the same demands of myself."