Solskjaer left United four years ago and Besiktas is his first job since his dismissal.
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He told BBC Sport: "Man United is my family and will always be part of me.
"In football, you don't feel sorry for anyone because we are privileged, absolutely 100% privileged to be able to work in clubs like this.
"But for me, it is hard to watch because it is your family that is struggling. It is never easy at the weekend when you look at the table."
Solskjaer admits he sale of Scott McTominay to Napoli surprised him.
He added, "Scott and Fred together, they were lads you would put your hat on every day to give 100%.
"How you can sell Scott is beyond me."