In the lyrics to the chant, which is set to the tune of the Stone Roses' 'Made of Stone', the 24-year-old - a £75m summer arrival from Everton - is deemed to have "a 24-inch penis".
The anti-discrimination group Kick It Out has described the chant as "offensive and discriminatory" for using the ethnic stereotype that black men are generally equipped with larger penises.
In a statement today, United confirmed: "Manchester United are speaking to the relevant authorities about the song and will act accordingly depending on the advice they're given.
"United have a zero tolerance stance towards any forms of racism. Greater Manchester Police have had no complaints about the song at all."
Lukaku, who was born in Belgium to Congolese parents, has scored seven times so far this season.