The National Enquirer and RadarOnline reported a 35-minute recording, apparently of the actor, making threats about former porn star Scottine Ross.
Ms Ross has taken legal action against Sheen, claiming he physically abused her and had sex with her without disclosing his HIV positive status.
Sheen has not commented on the reports.
Earlier this week, police officers served a search warrant on the New York headquarters of American Media Inc, the parent company of both RadarOnline and the Enquirer.
According to the warrant, the Los Angeles police investigation was triggered when Ms Ross made a complaint on 31 March saying she feared for her life after reading the reports.
On Thursday, the publications - neither of which have published the audio alleged to contain the star saying he would like to see a former fiancee "have her head kicked in" - refused to hand over the material to police.
Dylan Howard, the Enquirer's editor-in-chief and editorial director of RadarOnline, told Reuters the outlets had no plans to turn over documents or identify their sources.
He said the search warrant, signed by an LA County Superior Court judge, was illegal under both state and federal law preventing the use of such warrants against media organisations relating to "newsworthy" information.
He said: "We do believe that a judge did issue this order against the law, and that's why we will not be complying with its order."
In a televised interview in November 2015, Sheen said he had been diagnosed with HIV four years earlier.
The former star of Two and Half Men and films including Wall Street and Platoon admitted his history of drink and drug abuse was a "bad decision" but said it was "impossible" he would have passed HIV on to anyone else.
In December, Ms Ross - who was engaged to Sheen in 2014 before the relationship was broken off - filed a legal action against him accusing him of "physical, psychological and emotional abuse".

Tycoon Sir Terry Matthews, JoJo Mamam Bebe founder Laura Tenison and Cardiff Airport chairman Roger Lewis are among 10 who have signed a letter backing the case for remaining in the EU.
It highlights access to the European market and EU investment in skills.
The Leave campaign argues that business would still be able to trade with the EU after Brexit.
It also believes funding that comes from the EU to Wales could be replaced by Westminster from the savings of not paying for EU membership.
But in the letter, the business leaders argue: "Our membership of the EU is vital to the Welsh economy - giving Wales favourable access to a market of 500 million people, supporting competitiveness and innovation and spreading investment in infrastructure to all parts of Wales."
At the moment, 41% of exports from Wales go to the European Union.
That has risen from £4.7 billion worth of goods and services in 1999 to £5 billion in 2015.
Those who support leaving the EU claim it would allow exporters to focus more on growing markets further afield.
Exports from Wales to countries outside the EU have risen from £1.7 billion in 1999 to £7.2 billion  in 2015.
If Brexit does happen, selling abroad will be dependent on what trade deals can be negotiated with other countries.
Skills is one of the key areas for businesses and the letter goes on to say: "Investing in skills is so important to raise income levels and encourage further business growth, and in this decade, we will see £1 billion of EU funds invested in young people, training and skills."
Others who signed the letter include:
Advocates of leaving the EU argue the money saved from membership fees could be reinvested in other areas.
Reality Check: Would Brexit put 400,000 jobs at risk?
What does the EU referendum mean for Wales?
Businesses on Anglesey on the referendum
The independent think-tank, Institute for Fiscal Studies (IFS), has warned the savings from membership fees do not take any account of the potential damage to the economy of leaving the EU.
Most business surveys suggest that firms are, to a greater or lesser extent, in favour of remaining in the EU.
In April, aerospace company Airbus, wrote to its 6,000 workers in Flintshire warning about the risks of voting to leave the European Union.
Actor Charlie Sheen is facing a police investigation over claims he made threats against an ex-girlfriend, who is suing him for assault and battery.
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The Welsh economy is "stronger, safer and better off" in the European Union, a group of top business figures says.