The song has been heard at Old Trafford in support of the Belgian international, who signed for the Red Devils from Everton in a £75m deal during the summer.
To the tune of 'Made of Stone' by the Stone Roses, the chant goes: "Romelu Lukaku, He's our Belgium scoring genius, He's got a 24-inch penis, Scoring all the goals, B*****d to his toes."
Kick It Out has complained about the song as it refers to a racial stereotype that black men are better endowed than others.
A spokesman for the organisation said: "Kick It Out is aware of footage of alleged racist chanting by supporters of Manchester United that emerged on Wednesday evening (September 13).
"The lyrics used in the chant are offensive and discriminatory. Racist stereotypes are never acceptable in football or wider society, irrespective of any intention to show support for a player.
"We have contacted Manchester United regarding the issue and will be working closely with them and the FA to ensure that it is addressed swiftly. If we receive any reports relating to the discriminatory chant, those will be passed on to the governing body and the perpetrators can expect to face punishment."
According to The Independent, the Premier League giants are seeking advice on what steps to take in regard to the chant, which is not sung with abusive intention.
Lukaku has scored six goals in all competitions so far this season.