One of the doctors who treated Mr Mutharika said the president was “clinically dead” on Thursday after suffering a cardiac arrest.
State media are still reporting that he has been flown to South Africa for medical treatment.
If confirmed, his death would spark a constitutional crisis, analysts say.
According to the constitution, the vice-president takes over if the head of state is incapacitated or dies in office.
But Vice-President Joyce Banda and Mr Mutharika fell out after a row over the succession in 2010, and she was expelled from the ruling party.
Mr Mutharika’s brother, Foreign Minister Peter Mutharika, was chosen instead of Ms Banda to be the presidential candidate of the governing Democratic People’s Party in the 2014 elections.
The BBC’s Raphael Tenthani in the main city, Blantyre, says that ministers have been meeting all night to discuss the situation.
The doctors and ministers say that Mr Mutharika’s body was taken to South Africa while a decision is taken about what to do next.
Government sources have told the BBC that efforts to resuscitate President Mutharika had failed and that an official announcement is being prepared.
Mr Mutharika came to power in a 2004 election. Soon afterwards, he dramatically abandoned his United Democratic Front (UDF) party to form the DPP, after accusing leading UDF members of opposing his campaign against corruption.
Since being re-elected with a large majority in 2009, critics allege he has demonstrated an increasingly authoritarian streak.
The president has been under mounting pressure to resign, amid accusations of nepotism and economic mismanagement.
The criticism has led to a souring in relations with major foreign aid donors, especially the United Kingdom.
Last year, Mr Mutharika expelled the UK High Commissioner, Fergus Cochrane-Dyet, after a leaked embassy cable quoted the diplomat as saying that the president could not tolerate criticism.
The Malawian leader said he could not accept “insults” just because the UK was his country’s largest aid donor.
In response, the UK expelled the Malawian envoy to London and cut direct aid.
Malawi is one of the poorest countries in the world, with an estimated 75% of the population living on less than $1 (60p) a day.
The country has suffered shortages of fuel and foreign currency since the UK and other donors cancelled aid.