The Norwegian, who scored the winner in the Champions League final in 1999 against Bayern Munich, is now the club's permanent manager.
And he wants to bring back that type of success to the club, no matter what it takes.
"I think we've got to set that standard," Solskjaer told ESPN FC.
"We can do it one day [win the treble again]. It's going to be more and more difficult.
"Football has changed and there are more and more clubs with more and more money. In England, it's hard to get a top six place.