But Mr. Musk tweeted "I've only seen Nicole twice in three years, both times with many other people around. Nothing romantic"
Mr. Musk's comments came after the Wall Street Journal reported that his friendship with Mr. Brin had ended over the alleged affair.
Mr. Musk went on to say that he is still friends with Mr. Brin and that they were "at a party together last night!"
Citing people familiar with the matter, the Wall Street Journal said that Mr. Musk was engaged in a brief affair late last year with Ms. Shanahan.
This prompted Mr. Brin to file for divorce earlier this year and ended the long friendship between the two high-profile technology billionaires, the paper also said.
At the time of the alleged affair in December, Mr. Brin and his wife were separated but still living together, the Wall Street Journal said, citing a person close to Ms. Shanahan.
In a separate tweet, Mr. Musk said "WSJ [Wall Street Journal] has run so many bs hit pieces on me and Tesla I've lost count."
Even though they have a prenuptial agreement, Mr. Brin and Ms. Shanahan are currently negotiating a divorce settlement, which could be as much as $1bn (£830m), the paper said.
Mr. Musk is the world's richest person, with an estimated fortune of more than $240bn, according to the Bloomberg Billionaires Index.
According to the same index, Mr. Brin is worth around $95bn, making him the eighth richest person in the world.
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