Izetbegovic, 78, was rushed to a Sarajevo clinic last week after he fainted at home and fractured four left ribs.
He has already suffered two heart attacks in recent years.
"Internal bleeding in the chest occurred this morning and continued during the day," said Ismet Gavrankapetanovic, the head of a medical team monitoring Izetbegovic, on Thursday.
The team "is currently considering surgery, which would be limited given the patient's chronic heart weakness and serious condition," he said without elaborating.
A medical source added that surgery would be needed to save Izetbegovic's life.
The former president has suffered a series of complications including respiratory and circulation problems since Tuesday.
Elected chairman of Bosnia's collective presidency in 1990, Izetbegovic was a key figure during the country's 1992-1995 war.
He won worldwide sympathy by running the government from sandbagged buildings during the three and a half year long siege of Sarajevo by Bosnian Serbs under constant threat of their artillery and sniper attacks.
He held the Muslim seat in Bosnia's post-war presidency, which has a rotating chairmanship that also includes a Serb and a Croat representative.
Izetbegovic stepped down from the presidency in October 2000 due to failing health and his advanced age.
He was fitted last year with a pacemaker by Slovenian cardiologists, and has received treatment for his heart condition in hospitals in Sarajevo and Saudi Arabia.