The Red Devils forward is on international duty with Belgium.
Lukaku has struggled to hit form since his arrival last season from Everton for £75m.
The 25-year-old has scored 42 goals in 89 appearances, with nine of them coming under new boss Ole Gunnar Solskjaer.
Since the club legend’s arrival, the forward has been gaining confidence.
And footage has emerged on the club’s official Instagram channel which shows Lukaku has a high opinion of himself.
In the clip, the Belgian is taking questions from Facebook.
The 25-year-old is asked who the fastest player is in the United squad.
With a cheeky smile, the forward gives his confident answer.
Lukaku’s claim comes as:
“Rashy would take you in a race”
Man Utd fan
Lukaku holds his hand up, choosing himself as the fast player.
And the forward took the chance to answer his critics.
“People call me slow,” Lukaku added.
The forward finishes off with a laugh.
Since being posted earlier today, this footage has been viewed nearly 500,000 times.
But the United faithful were not convinced, suggesting another forward was quicker.
“He’s not slow but no way is he faster than [Marcus] Rashford,” one supporter said.
Another commented: “You’re the slowest.
“Rashy would take you in a race.”
While a third simply said: “I find this hard to believe.”
But United could see a former player join a Premier League rival.