Alba, 29, was a regular for La Roja, amassing 66 caps since making his debut in 2011 but his international future is under real doubt with Enrique at the helm.
The pair reportedly failed to see eye to eye during his final season at Barcelona and with his recent squad selections, questions have been raised over their relationship
A regular under predecessor Julen Lopetegui and a starter at the World Cup in Russia, Alba assisted three goals in Barca's 4-2 win over Tottenham on Wednesday.
"By rule, I don't talk about players who are not on the list," Luis Enrique said at Thursday's news conference. "But I've always left out players based on sporting reasons.
"Unfortunately, I can only bring 23 players knowing that there are another 20 players that could play and do well for the national team."