The Belgian striker has been adapting to life at Old Trafford since signing for the Red Devils from Everton in the summer transfer window.
However, he has been singled out for failing to do enough to prevent some sloppy goals which Manchester United have conceded in recent weeks.
And former Red Devils midfielder Scholes has told Lukaku to step his game up when he is tasked with helping Manchester United keep things tight at the back from set pieces and in other defensive situations.
Speaking to BT Sport on Saturday night, Scholes said: “There’s a lack of leadership there really.
“There should be a captain or a centre-half saying [to Lukaku] to concentrate. He doesn’t look ready. He doesn’t look like he’s interested in defending.”
Lukaku suffered a head injury in the first half of Manchester United’s goalless draw with Southampton on Saturday and it has not yet been confirmed how long he will be out of action for.
The Red Devils are set to return to Premier League action with their first game of 2018 when they take on Everton at Goodison Park on Monday.
All eyes will be on Old Trafford in the coming weeks as Jose Mourinho considers bolstering his Manchester United squad in the January transfer window.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news