According to police documents seen by CNN, police opened an investigation after Khan vowed to "take action" against the head of police and a female magistrate during a speech in Islamabad on Saturday.
"Listen Director Inspector General (of police), we're not going to let you go, we're going to file a case against you. And madam magistrate you should also get ready, we will take action against you," Khan told hundreds of his supporters during a rally held in support of his former chief of staff, Shahbaz Gill, who was arrested earlier this month on sedition charges after he urged soldiers to disobey orders from military leaders.
Khan has alleged police have tortured Gill while in custody, claims that have gained widespread traction among the former prime minister's supporters. Islamabad police have denied Khan's allegations, telling CNN on Saturday that Gill has not been tortured.
On Sunday, Islamabad police tweeted a video of Khan's speech, saying: "Anyone making threats or accusations will be dealt with according to the law."
Khan has not been arrested and has not commented publicly on the investigation. His Pakistan Tehreek-e-Insaaf (PTI) party said the probe was based on "frivolous allegations with no legal grounds."
Khan's team on Monday filed a pre-arrest bail application in Islamabad's High Court, the PTI's media coordinator, Raoof Hassan, told CNN.
"Now if they have to arrest him they will have to have the pre-arrest bail dismissed. This will now become a legal battle," Hassan said.
Hundreds of Khan's supporters gathered outside his home on Saturday night following reports of the police investigation, vowing to "take over" the capital if he was detained.
Live broadcast ban
As tensions grow, Pakistan's Electronic Regulatory Authority (PERA) issued an order late Saturday banning Khan's speeches from being broadcast live on television, citing "hate speech."
Khan was "leveling baseless allegations and spreading hate speech through his provocative statements against state institutions," a statement from PERA said, adding the comments were "likely to disturb public peace and tranquility."
Channels can air his recorded speeches, according to the order.
In a Twitter post Monday, Khan accused the government of temporarily blocking YouTube during his speech on Saturday. "This is not only a gross violation of freedom of speech but also negatively affects the digital media industry and the livelihoods of many," he said.
CNN has reached out to YouTube and the Pakistani government for comment.