"I'm not going to Twitter, I'm going to stay in TRUTH," Trump was quoted as saying by Fox News.
TRUTH Social is a social network created under the patronage of the former US leader.
He also expressed confidence that Musk can make Twitter better.
Earlier it was reported that Elon Musk signed a deal to buy Twitter for $44 billion.
Twitch, Twitter, Facebook, YouTube, and Instagram suspended Trump's accounts for varying periods of time due to his statements about the January 6 riots in Washington.