"I would be, if he wanted to buy it," Trump told reporters on Tuesday when asked if he was open to Musk buying the platform.
"I have met with owners of TikTok, the big owners," Trump added.
"So, what I am thinking about saying to somebody is 'buy it and give half to the United States of America'".
Elon Musk has been given the green light by Donald Trump to buy TikTok if he wants. (AP PHOTO)
The short video app used by 170 million Americans was taken offline temporarily for users shortly before a law that said it must be sold by its Chinese owner ByteDance on national security grounds, or be banned, took effect on Sunday.
The Chinese company is under pressure from Washington to sell its popular video-sharing app in the United States.
Bloomberg News reported last week that Chinese officials were in preliminary talks about a potential option to sell TikTok's operations in the US to Musk, though the company has denied that.
Trump on Monday signed an executive order seeking to delay by 75 days the enforcement of the law that was put in place after US officials warned that under Chinese parent company ByteDance, there was a risk of Americans' data being misused.
TikTok remained unavailable to download on Apple and Android devices in the United States on Tuesday afternoon.
Free speech advocates have opposed TikTok's ban under a law passed by the US Congress and signed by former President Joe Biden.
The company says US officials misstated its ties to China, arguing its content recommendation engine and user data are stored in the United States on cloud servers operated by Oracle, while content moderation decisions that affect American users are also made in the US.
Musk, who spent more than $US250 million ($A399 million) to help Trump win November's presidential election, has said there was an "unbalanced" business environment between the US and China.
"I have been against a TikTok ban for a long time, because it goes against freedom of speech. That said, the current situation where TikTok is allowed to operate in America, but X is not allowed to operate in China is unbalanced," Musk, who owns social media platform X, said over the weekend.
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