"Contact was established with the fugitive 10 days ago and intensive negotiations for his surrender are being held," said a report in the Bosnian newspaper Nezavisne Novine, quoting an unidentified source in the Bosnian Serb interior ministry.
General Mladic, former military chief of the Bosnian Serbs, is wanted for genocide in connection with the 1995 Srebrenica massacre of 8,000 Muslim men, the single worst atrocity in Europe since World War II.
He is understood to have been hiding out in Serbia.
Negotiations were being conducted by close aides of Serbian Prime Minister Vojislav Kostunica and by Bosnian Serb Interior Minister Darko Matijasevic, the report said.
Former Bosnian Serb general Mladic, 63, and his political leader Radovan Karadzic, 60, have been at large since they were indicted by The Hague-based international war crimes tribunal 10 years ago for crimes committed during the 1992-1995 Bosnian war.
"Things are happening in Belgrade that could make the people of Bosnia happy, and speed up the march towards membership of the European Union," the newspaper quoted Bosnian Serb police spokesman Radovan Pejic as saying.
But Mr Pejic told AFP that his statement was "misinterpreted" by the newspaper, saying he was simply referring to "good collaboration" between Serbia and Bosnia.
On Friday, the UN tribunal in The Hague warned Serbia the international community was becoming increasingly frustrated with its failure to bring about the arrest of Mladic and Karadzic.
Chief prosecutor Carla Del Ponte has said she believes Mladic is being sheltered by the Serbian army and that Karadzic is somewhere on the border between Bosnia and Montenegro -- Serbia's union partner.
Serbia-Montenegro's Defence Minister Zoran Stankovic warned that the country might be excluded from joining European and Atlantic groupings such as the European union and NATO if Mladic was not arrested by a "certain deadline."
Sunday's report here also said another wanted man, Stojan Zupljanin, was likewise the subject of surrender negotiations.
Zupljanin, a senior police officer during the 1992-1995 war, has been charged with war crimes.