Broadcasting watchdog Ofcom is considering 20 complaints about ITV show Lorraine.
The presenter also said the ops are an “easy option” for people losing weight.
Kelly made the comments while discussing a study that claimed the NHS should be carrying out 10 times as many gastric band procedures.
The 56-year-old, who went from a size 14 to a 10 in 2014 after taking Zumba classes, said the procedures would “cost a fortune”.
She added: “Don’t you think it is giving people the easy option? Oh, it’s OK, I will just guzzle deep fried lard because someone will just come along and give me an operation.”
But viewers were furious at her comments on the May 12 show.
Layla Whitehouse said: “I think you need to rethink your choice of words! Disgusting way to talk about people having a weight-loss operation.”
Too many people having weight-loss surgery could bankrupt the NHS
Dr Hilary Jones, who was a guest on the programme, claimed too many people having weight-loss surgery could bankrupt the NHS.
He said: “People can lose the weight through natural means rather than invasive surgery. “So why not address that and help everybody to stop getting fat in the first place?”
But the research by Bristol University scientists claimed gastric band ops would save the NHS cash.