The 22-year-old was signed by City in 2012 from Deportivo La Coruna, and was promoted to the senior team two years later, but he spent the majority of the career on loan at New York City, Girona, Mallorca and NAC Breda before signing a five-year contract for PSV last summer having made just three first-team (cup) appearances for the Premier League giants.
However, manager Pep Guardiola wants another left-back with Benjamin Mendy struggling for fitness since completing a £50 million move from AS Monaco two summers ago.
Fabian Delph is set to leave this summer, leaving City with Aleks Zinchenko as their only fit senior player in the position.
Paris Saint-Germain and Arsenal have shown interest in signing Angelino, with PSV ready to let him go for £23 million, but City are considering triggering the £5.35 million buy-back clause inserted in his sales and they have first option on him.
Angelino ended last season with a goal and 10 assists in 41 games, and the Spain youth international could prove to be a quality addition to a Guardiola side that could do with more depth and quality competition.