The priority was reportedly given to the Binance, Saudi Arabian and Qatari funds, which had invested at least $250 million or higher in the social platform.
The move comes after the US Treasury Department reportedly started examining whether it had a legal ground to conduct a probe into Musk's ties to foreign governments and investors.
On Monday, US Senator Chris Murphy urged a congressional panel to launch an investigation into investments in Twitter by Saudi Arabia's Kingdom Holding Company after Musk acquired the social media company. Murphy said the United States had to be concerned about Saudi investments in Twitter due to their interest in repressing political speech and influencing US politics.
The US billionaire closed the $44 billion acquisition deal last Friday. He tweeted on Sunday that "the whole verification process is being revamped right now."