It comes as new BBC head Tim Davie said he is leading a fresh drive at the BBC for the corporation to become more impartial. He said this would mean BBC staff would face new rules requiring them to watch what they say on social media platforms such as Twitter.
Mr Lineker – who is outspoken about his own personal views – has previously denied being concerned about the push for impartiality.
A BBC spokesperson said the retired sports star and Match of the Day presenter will not be required to adhere to the new rules at all.
The spokesman told the Telegraph: “Gary is not involved in any news or political output for the BBC and as such, any expression of his personal political views does not affect the BBC’s impartiality.”
Sources said other staff who are not involved in the BBC’s news and current affairs output will also be exempt from the social media rules.
It is not currently clear what Mr Davies’ new rules will be – the BBC already had guidelines on social media impartiality for its news staff.
Mr Davies said: “If you want to be an opinionated columnist or a partisan campaigner on social media then that is a valid choice, but you should not be working at the BBC.
“We’ll take action in coming weeks, but to be clear, there will be new guidance on how we best deliver our impartiality guideline; new social media rules, which will be rigorously enforced; and clearer direction on the declaration of external interests.
“Our research shows that too many perceive us to be shaped by a particular perspective.
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Mr Lineker has previously been critical of Brexit on his Twitter account, calling for a ‘People’s Vote’ – a second referendum – on at least one occasion.
The TV presenter said in one tweet: “It’s very clear now that there is no good deal. There’s this rotten deal or an even more painful no deal.
“Surely It’s time our politicians did what’s right for this country and what’s right for the people of this country for the sake of this country. #PeoplesVote.”
In 2018, Mr Lineker also appeared to criticise then-Labour leader Jeremy Corbyn for failing to overtake the Conservatives in national polls.
He wrote: “Imagine how hopeless you’d have to be to still be behind the Tory party in the polls. The absolute state of our politics.”
Former BBC guidelines state staff should not publicly reveal how they vote or show support for any political party.
The rules also said staff should not “advocate any particular position on a matter of public policy” or any other matter considered controversial.
The rules may not apply to BBC staff who are personally affected by a particular matter, or are not involved in news or current affairs.