Manchester United romped to a 3-1 victory over Huddersfield Town without their forward trio on Boxing Day.
A Nemanja Matic goal and two strikes from Paul Pogba were enough to see off Huddersfield.
Lukaku has been away on compassionate leave, while Sanchez has ben suffering an injury.
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Martial fell ill before the match, Solskjaer said, but may be fit for Saturday’s home tie with Bournemouth.
Asked if he will draft the trio back into his side, the Norwegian said: “Not a bad front three to come in and knock on the door.
“It will be great to get them back.
“Maybe we’ll change the front three.”
Sanchez had returned from South America before Christmas and Solskjaer said: “He’s had two days of good fitness work.
“Hopefully he can join in training with the ball as soon as we get back in again.
“He is touch and go for Bournemouth but he will definitely be involved at Newcastle.
“I’ve not had time to sit down and speak with him in that much detail but he’s eager to get back on the pitch, at it seems to me he is a workaholic.”
Solskjaer seemed particularly coy about Martial ahead of the game.
“He must have had a bad chef over Christmas,” Solskjaer told MUTV.
“If it’s food poisoning or something. I don’t know, but he has fallen ill over Christmas.”
It was suggested the player had flown back to Manchester on Tuesday night after being in Paris.
Manchester United have now won two games on the bounce under Solskjaer, who is tasked with holding the fort until the end of the season – at which point the Red Devils will appoint a new manager.
On the win over Huddersfield, the manager added: “You need momentum. The next two games will be massive for us.
“Coming into those games with confidence is great.
“This is Manchester United. When you score a first, you want a second. When you score a second, you want a third. We wanted a clean sheet.
“Every team is built on that foundation. We’ve conceded from two set-pieces so far. We’ll make sure we get a clean sheet soon.”
Asked of his experience managing at Old Trafford for the first time, Solskjaer said: “I’ve not got used to it yet. It’s humbling knowing I’m leading this team out.
“Let’s see if I get used to it. I captained a couple of games but this was very different.
“They are the best fans in the world. I had such a great relationship with them. It was probably more emotional for my family in my box as I was focussed on the game.
“I was surprisingly calm all day. The lads have helped me settle in really quickly.
“Dave’s [de Gea] save was the defining moment, one of the best saves I’ve seen. I could see it going top corner and he stretches his second arm out.
“Paul [Pogba] knows he can score more goals and create chances. He had a few assists last week. He’s happy now.”
