Despite the potential coronavirus-related quarantine headaches, the Red Devils boss allowed the 30-year-old to fly to Spain to be with his partner.
Dean Henderson has had a run in the side in the absence of United's number one, who has been inconsistent this season.
He impressed in Sunday's 2-0 win against Premier League leaders Manchester City but was criticised for allowing an injury-time header to beat him as AC Milan snatched a 1-1 draw in the first leg of the last-16 tie in the Europa League on Thursday.
Asked on Friday about De Gea's availability for the visit of West Ham, Solskjaer said: "David is back in Manchester. He is quarantining or self-isolating".