Sanchez has been out of action for several weeks with a hamstring problem but looks on course to be back on the pitch sooner than expected. Martial, meanwhile, was ruled out of the Boxing Day win over Huddersfield as a result of illness, with Lukaku also absent.
Solskjaer said this morning that Lukaku, Sanchez and Martial are in contention to feature against Bournemouth on Sunday. Smalling still out but could be back for Tottenham on Jan. 13.— Rob Dawson (@RobDawsonESPN) December 28, 2018
The trio will have a few days to train before the Bournemouth game to improve their fitness.
In further comments published by the Daily Mail, the interim boss urged the trio to take their chance in the way that Paul Pogba has done: "Paul has done it. My chats with Anthony, Romelu, Alexis, I'm here to guide them on the path, and it's up to them to do it on the pitch.
"It's up to them when they get a chance, that's the name of the game as a footballer. You've got to do it yourself. I gave some guidelines of course on expression, freedom of expression, but that's how I've always been as a manager," he added.
"You can't tell the players what to do in this position, just enjoy playing for this club, that's the best time of your life - but it's not a bad time to be manager for a while."
Solskjaer has refused to take credit for Pogba's resurgence, praising the Frenchman's quality.
"I think Paul's a top, top player," he added. 'He's one of the top players in the world. Attacking wise, he's done really well but he's a big lad who can win headers and tackles. He's been the same as the others," he explained.
"The attitude has been perfect and that's key; you should be tired towards the end of every single game. He's been top-class and of course he's someone that we're looking to build a team, but there are so many quality players."
Despite uncertainties over Antonio Valencia's future at the club under former manager Jose Mourinho, Solskjaer has also confirmed that the Ecuadorian veteran, who has not played in the Premier League since September, will remain captain.
"When he's properly fit and playing, he'll wear the armband," Solskjaer said, via ManUtd.com.
"He's going through a couple of tough sessions now to get him ready for the busy period coming up. When you look at Antonio, there are not many better right-backs going forward with his abilities so, yes, you'll see him wearing his armband."