A number of the away fans reprised the song after the Belgium striker scored the only goal of the game at St Mary's Stadium, before "we're Man United, we sing what we want" was also heard from the stand.
The distasteful chant has been described by anti-discrimination body Kick It Out as "offensive" and both the club and Lukaku issued pleas this week for fans to refrain from singing it.
United have now said they are speaking with police to identify those who "disrespected the player's wishes" by ignoring his request.
A club spokesperson told Omnisport: "Manchester United has a zero-tolerance stance on offensive chanting and behaviour.
"The club and player have been clear in asking for an end to the chant.
"The club has worked with relevant bodies and supporters groups in trying to eradicate any offensive behaviour and will take further action against individuals if this continues.
"The club is in discussion with the police and has asked for CCTV footage from Southampton and will try to identify those who disrespected the player's wishes not to sing the song."
The 1-0 win lifted Jose Mourinho's side to 16 points from six matches, level with Manchester City, who lead the table on goal difference.
It was Lukaku's eighth goal in as many games since signing from Everton for a reported £75 million fee in July.