Kick It Out described a song, which makes reference to the size of Lukaku's manhood, as "offensive and discriminatory" with racist undertones in a letter to United earlier this week.
"Racist stereotypes are never acceptable in football or wider society, irrespective off any intention to show support for a player".
The Spaniard, who managed Lukaku at Everton, has been impressed with the 24-year-old's development since his £75m move to Old Trafford this summer and has already seen a "big difference" in his game.
'Great backing since I joined United, ' the striker said.
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"Fans have meant well with their songs but let's move on together", he said, signing off with the hashtag "RespectEachOther". During the first half a new chant was heard about the Belgium forward, but the words had been slightly adapted.
And Old Trafford chiefs are understood to have really pushed the boat out to ensure the Belgium global did not end up back at Stamford Bridge.
On Friday, boss Jose Mourinho was asked about the chants to which he replied: "Don't ask me these questions".
Via The Times, Kick It Out released a statement about the song which was heard in both United's 3-0 UEFA Champions League win against FC Basel last week and also the 4-0 home victory against Everton on Sunday.
It has not yet been confirmed how long Pogba will be out of action for as Manchester United look to continue their strong start to the season against Southampton in the Premier League this weekend.