Sanchez, 30, and Lukaku, 25, appeared to fall out of favor under former manager Jose Mourinho at Old Trafford.
Solskjaer said he has given them "guidelines" on expressing themselves but that it is "up to them" to perform.
Sanchez last featured for United against Crystal Palace in November because of a hamstring injury.
Lukaku, a £75m signing in 2017, has not played in Solskjaer's first two games in charge but has returned to training before Sunday's visit of Bournemouth in the Premier League.
He has scored six goals in 16 league games this season, while Sanchez, who joined from Arsenal in January, has one goal in 10 matches.
"Romelu, Anthony [Martial] and Alexis they were light, light [training] yesterday so hopefully they can join part of the training today and let's see after how they come through," Solskjaer said on Friday.