Sterling said the incident occurred when he retrieved the ball near the home supporters during Saturday's match at Stamford Bridge.
Colin Wing was one of four fans suspended and is believed to have launched racial insults at Sterling. However, the 60-year-old denies he said such things but apologized for shouting other forms of abuse at the City player.
"I'm deeply ashamed by my own behavior and I feel really bad. But I didn't call him a black c---, I called him a Manc c---," Wing said in an interview with the Daily Mail.
Police launched an investigation into the matter but have yet to make any arrests despite speaking with Wing twice Saturday after the match. Although no formal charges have been laid, Wing said he lost his job because of the incident.
"Nobody around me said they heard anything," he added. "I want to apologize unreservedly to Raheem and hope he can be a better man than I am by accepting it.
"I offer him an unreserved apology. Even if it wasn't racist, it's not right what I said. Even the swearing is bad - but I got carried away.
"I was completely out of order, but I've lost my job and my season ticket now so everybody's got what they wanted. So why can't they leave me alone?"
Sterling took to social media on Sunday to condemn the incident and highlight how the media plays a role in fuelling racial abuse.
Manchester City manager Pep Guardiola has yet to speak to Sterling about the alleged abuse but praised the 24-year-old's response to the incident.
"It's everywhere," Guardiola told reporters on Tuesday, referring to racism, according to BBC Sport. "People focus on football but it's not just in football, unfortunately.
"It's to immigrants and refugees all over the world, when once in our lives we were all immigrants and refugees in our family. That's why they have to fight every day.
"We have to fight to make a better situation for everyone. The message for the politicians is for them to be tough on human rights and we have to defend democracy in the best way."