The Spaniard had to self-isolate after travelling to Spain for family reasons.
De Gea will return next week as long as he tests negative for Covid-19.
Speaking to Sky Sports on Sunday, Ole Gunnar Solskjaer said: “David De Gea is finishing his self-isolation period today.
“He will hopefully be back in training tomorrow after his [Covid-19] test. We’ve got to follow all the protocols so hopefully the test comes back the way we want it.”
Last week, De Gea was given a temporary leave of absence by the manager to fly back home to Spain for the birth of his baby daughter.
Dean Henderson has started in four of Manchester United’s last games across all competitions, conceding just 1 goal and keeping 3 clean sheets.