Gary Lineker described the accusations, which he called northern voters “racist bigots”, as “outrageous and dangerously provocative”.
The recently reinstated match of the day host reappeared on Twitter in response to comments from Conservative MP Jonathan Gullis.
During an interview with Channel 4 News, Gullis said he was not concerned about upsetting members of ‘Twiterati’.
Speaking about Prime Minister Rishi Sunak’s recent legislation on small boats, he said: “As far as I’m concerned, it’s certainly difficult and upsets all the right people in the right places.
“Let’s be clear, when I say annoying people, I mean Twitterati, North Islington Wokerati, those champagne socialists who talk all day.
“These are the people I don’t care to upset because these are the people who want to call people here racist bigots, Nazis like Gary Lineker did.”
Responding to the clip, another Twitter user wrote: “I don’t think Gary Lineker actually directly referred to Red Wall voters as ‘Nazis,’ Mr. Gullis.”
Lineker also responded by writing, “No, he didn’t and never would. It’s outrageous and dangerously provocative.”
It comes after BBC chief executive Tim Davie announced that Lineker would return to present Match of the Day on Saturday.
Mr Davie apologized for a recent row over impartiality sparked by one of the presenter’s previous tweets and announced a review of the broadcaster’s social media guidelines.
Lineker “will abide by editorial guidelines” pending a review of the BBC’s social media policy, Davie said.
The row erupted after Lineker was taken off the air for a tweet comparing the language used to introduce the government’s new policy on asylum seekers to the language of 1930s Germany.
He was then asked to “take a step back” from the popular soccer show, prompting a boycott from other MOTD pundits and commentators.
The PA news agency understands that earlier on Tuesday, BBC staff were invited to lunch sessions in Salford for Mr Davie and the director of public affairs.
Meanwhile, Ofcom chief executive Dame Melanie Dawes also told the Digital, Culture, Media and Sport Committee meeting that the past week has been “a really tough episode for the BBC” but that she hopes “they can deal with it”.
Since the altercation, Lineker has changed his Twitter profile picture to a picture of himself next to a quote from George Orwell that appears on the wall outside the BBC.
“If freedom means anything at all, it means the right to tell people what they don’t want to hear,” the quote reads.