The Belgian star, 25, is unlikely to return before the end of the month and could miss United's busy festive schedule.
Lukaku has been away from Old Trafford all week and could miss the two Premier League games against Cardiff and Huddersfield.
Speaking during his first press conference as caretaker boss, Solskjaer confirmed: “Yes, he [Romelu Lukaku] has had a couple of days off, so I've not seen him yet."
Meanwhile, the Norwegian boss revealed he also hasn't seen Alexis Sanchez – who reportedly won an ill-considered bet regarding Jose Mourinho's sacking – yet
Solskjaer added: "I've not seen Alexis because he's on his way back as well, so I'm looking forward to seeing them.
"That was decided before me, so that's fine."
Solskjaer also revealed he would love the United job on a permanent basis – after only being given the job until the end of the season.
The ex-Molde chief said: “When you get a job like this and they ask you to sign for six months you say yeah.
“I’m happy to help out and my job now for the next six months is to do as well as I can and move the club forward as well as I can.
“I understand there are so many managers who would love to be manager of Manchester United and I am one of them.
“But it is not something we've talked about, they'll do a process now for the next six months.”
Solskjaer went on to say he wants his stars to play in the right way – and that's the most important thing for now.
He added: “I think the first thing is the first game, think about getting my principles into the boys, get the players to understand how I want them to play and let's take the results later on, see how many points we can gather.
“This club has made many, many points before but I'm not going to set that target now.
“My job is to help the players, make them grasp the opportunity. They all want be part of Manchester United."
Solskjaer also lauded Sir Alex Ferguson for his influence on him during his time as a player.
The Norwegian said: “He's influenced me with everything to be fair, the way he's dealt with people the way he was manager of the club, how he kept 25 international players happy and hungry wanting to improve.
"But also the staff in and around the place, he's been my mentor but I didn't understand early on he'd be my mentor.
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