Anti-discrimination group Kick It Out has described the chant, which suggests that the Belgian has "a 24-inch penis", as "offensive and discriminatory" for using the ethnic stereotype that black men have large penises.
United have since said that they are "seeking advice" on how to handle the situation but the 'MUFC Songs and Chants' supporter group have said that the song will continue for the time being as it is "not a negative chant".
In a statement released to The Sun, the group said: "This chant is not a negative chant, it's a stereotype, it doesn't mean it's racist.
"Does anyone know how Lukaku feels about this? He clearly hasn't come out and said he doesn't like it, we all know the players look at social media so he surely must have seen it.
"If Romelu Lukaku comes out and says he doesn't like it then we all as Manchester United fans should do as he asks and stop singing the chant, but until then keep singing this chant about a hypothetical body part and have fun singing it."
Lukaku, a £75m summer signing from Everton, has yet to comment on the furore.