The 18-year-old, who joined the Red Devils from Real Madrid in September 2020, has made 25 appearances for his side's Under-23s, scoring three times and contributing six assists in the process.
Fernandez has been training with the first team over the international break, though, and was pictured alongside Cristiano Ronaldo during the Portuguese's first session back at the club.
According to AS, Solskjaer has been impressed with the teenager, who could soon be in contention to make his first-team debut for the 20-time English champions.
The report claims that Fernandez's progession has been 'dizzying', with the youngster quickly becoming an important player for the Under-23s after featuring at Under-18 level.
The Spaniard came through the youth system at Deportivo La Coruna before moving to the Bernabeu.