Such a step would mark a radical change in Serbian policies, and could be the diplomatic breakthrough that helps to end the Bosnian conflict.
Mr Milosevic discussed the possibility of recognising Bosnia at a meeting in Belgrade this week with Muhamed Filipovic, the Bosnian ambassador to Switzerland.
It was the first known direct contact between Mr Milosevic and a Bosnian representative since the war started in April 1992.
Bosnia's Foreign Minister, Irfan Ljubijankic, termed the meeting "an exploratory mission" and cautioned that it had failed to produce any mutually acceptable proposals.
The Bosnian President, Alija Izetbegovic, at a news conference last night, said the meeting came at Mr Milosevic's initiative and did not signal any softening of Bosnia's positions. "We will stand and fight," he said. "We are in favour of one integrated Bosnia."
But political sources in Belgrade said Mr Milosevic had continued an indirect dialogue with the Muslim-led Bosnian government by holding talks with a special envoy of President Suharto of Indonesia, a country sympathetic to Bosnia. Serbian recognition of Bosnia would not end the war immediately because Mr Milosevic, having broken relations with the Bosnian Serbs for rejecting a peace plan last year, has lost the ability to influence the hardline Bosnian Serb leadership.
The Bosnian Serbs control 70 per cent of Bosnia and would rather have their own independent state or union with Serbian rebels in Croatia than see Bosnia restored as a united state.
If Mr Milosevic recognised Bosnia, he would still insist on the Bosnian Serbs' right to self-rule within a highly decentralised Bosnian state. He would also not be committing himself to ensuring that Muslim refugees, expelled by the Bosnian Serbs from their native areas, could return home. The latest tentative steps towards a peace settlement could be derailed by fighting in Bosnia. A four-month ceasefire, due to expire on 1 May, has almost completely broken down in recent days, with battles raging in the Majevica mountains near the Bosnian government-held city of Tuzla.
Mr Milosevic is contemplating recognition of Bosnia partly because he wants an end to United Nations' sanctions on Serbia. In a sign that the Bosnian government is willing to assist Serbia on this issue, Mr Ljubijankic said Bosnia welcomed a Russian initiative to suspend the sanctions in parallel with Serbian recognition of Bosnia.
One obstacle to a deal is that Serbian recognition of Bosnia and Croatia would appear, from a Serbian point of view, to defeat the whole point of almost four years of war in former Yugoslavia.
Gathering all Serbs into a single state, and not leaving some at the mercy of Croats and Bosnian Muslims, used to be the central theme of Mr Milosevic's rhetoric.
However, there is evidence that the pressure of war and sanctions, and the desire to shore up his power base in Serbia, have caused Mr Milosevic to revise his strategy. Under his orders, Serbian state propaganda has ceased to beat the nationalist drum as violently as in the past.
The most likely explanation is that Mr Milosevic is preparing public opinion for a far-reaching change in Serbian policies.Reuse content