The Red Devils have been asked to consider banning the song, which is sung to the tune of 'Made of Stone' by the Stone Roses and has been heard several times since the Belgian's move from Everton this summer.
Anti-discrimination group Kick It Out has described the chant, which suggests that Lukaku has "a 24-inch penis", as "offensive and discriminatory" for using the ethnic stereotype that black men are particularly well-endowed.
"Great backing since I joined #MUFC," the 24-year-old was quoted as saying on Man United's official Twitter account. "Fans have meant well with their songs but let's move on together. #RespectEachOther"
Lukaku has scored seven goals in as many games for his new club in all competitions.