The host jokingly referred to the Premier League new boys as Sheffield Wednesday during the show, apparently in reference to a Twitter exchange with a fan earlier in the week.
Many fans saw the funny side but, judging by the reaction from some supporters, it seems not everyone shares his sense of humour.
Posting on a fans’ forum, one person wrote: “Gary just called us Sheffield Wednesday – what a plank.”
Another commented: “Ooh dear Gary, let me explain. Sheffield Wendy are in a league BELOW us. Tut, tut, and you call yourself a professional football pundit. Let’s hope you improve next week!”
Others branded the ex-England striker ‘unprofessional’ and ‘amateur’, with several opting for much ruder epithets, and one woman even said on Facebook that she had made a complaint about him to the BBC.
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But some Blades fans accused their fellow supporters of being oversensitive and ‘so easy to bait’.
“It’s hilarious seeing grown men get so upset by what was clearly a joke. Who cares, we’re in the Premier League,” said one fan, who appeared to have seen the funny side.
For those wondering, a Sheffield United fan called Philip Backhouse had tweeted Lineker to say: “So don’t forget it’s Sheffield United, United, The Blades or SUFC. Not Sheffield.”
The presenter responded: “I’ve spent my whole life in football. Do you think for one moment that I’d make that sort of error?
“Wishing you well for the new Premier League season and, what’s more, I think Wednesday might surprise a few people.”