His comments come after he was banned from Match of the Day following his criticism of the previous government’s immigration policies.
BBC bosses were under pressure to sack Lineker over comments he made at the time, in which he likened the Conservative government’s immigration policy to Nazi Germany, and he had been told the previous year by the broadcaster’s director general, Tim Davie, to stay out of politics.
The BBC’s highest-paid star has previously defended his political tweets, saying he continues to speak out on social issues “so that I can look at myself in the mirror at night”.
Musk won the battle to buy Twitter for $44bn (£35bn) in 2022 after Twitter dropped its opposition to the Tesla billionaire.
He promised to build Twitter “better than ever” and protect it as “the digital forum where issues critical to the future of humanity are debated.”
Since then, he has scrapped Twitter’s trademark bird logo, replacing it with an X, introduced a blue check mark and a subscription service for other premium features.
Musk has previously claimed he was led to buy the company in the name of free speech after fearing his transgender daughter had been infected with a “woke mind virus” cultivated on the social media platform.