Musk - who has been named TIME's 2021 Person of the Year - insists there is no other woman in his life at the moment, and his commitment to his space tourism project and desire to reach Mars mean that there isn't much time for him to meet new people.
Discussing life at his Starbase headquarters, he said: "This place is basically like a technology monastery, you know. There are some women here, but not many. And it's remote."
Musk - who has been married on two occasions to his college sweetheart Justine Miller and to British actress Talulah Riley - was apparently the subject of a recent song by Grimes.
Grimes released a new song titled Player of Games, which seemingly alludes to her former partner.
In the lyrics, she sings, "I'm in love with the greatest gamer, but he'll always love the game more than he loves me," before going on to add, "Sail away to the cold expanse of space, even love couldn't keep you in your place".
Before making his first million at the age of 27, Musk was an avid creator of video games, with the entrepreneur claiming on Twitter that his tenure at Rocket Science Games was a "night job".