The May 11 elections were called after Kostunica clashed with his former coalition partners, the DS and reformist G17-Plus party, over ties with the European Union after most of the 27-nation bloc recognised Kosovo.
"Radicals the favourites", read the main headline in Glas Javnosti, the nationalist newspaper.
Tomislav Nikolic, the acting Radicals leader, told another daily newspaper he was confident his party would link up with Kostunica's Democratic Party of Serbia (DSS).
"The DSS and SRS will create a government very soon," Nikolic said.
"I expect to begin negotiations with Kostunica on a new coalition as early as May 12 and to form a government in the shortest possible period.
"The most important thing for me is that the SRS and DSS form a government and put into effect a programme which has already become our joint ideology," Nikolic said.
Vojislav Seselj, the founding leader of the SRS, is currently being tried at the United Nations war crimes tribunal for war crimes committed by his SRS volunteers in a bid to create a "greater Serbia" between 1991 and 1993.
The DSS has yet to rule out such a coalition, which together with the Socialists, could give the nationalist bloc a majority of up to 15 deputies in the 250-seat parliament, according to surveys.
Such a government would freeze co-operation with the UN's International Criminal Tribunal for the former Yugoslavia (ICTY).
Belgrade's hopes of joining the EU depend on co-operation with the ICTY, which is still seeking four Serbian fugitives including Ratko Mladic, the former Bosnian Serb wartime general who is wanted for genocide.
Kosovo unilaterally declared independence from Serbia on February 17, causing deep anger among Serbs who consider the southern territory the cradle of their history, culture and religion.
Kostunica, a moderate nationalist who has since turned increasingly hardline, has made the fight to keep Kosovo within Serbia the cornerstone of his re-election bid.
The DSS leader's harshest campaign rhetoric has been dished out to his former coalition partners whom he has labelled "traitors" for signing an EU pact he says is tantamount to Serbia recognising Kosovo.
Tadic and his DS party have hit back, saying such "lies" and "deceit" were responsible for stirring up hate that has led to a series of death threats against the Serbian president.
"Kostunica will never be the prime minister in this country again," Tadic told thousands of supporters at a rally in Belgrade's main Republic Square on Wednesday.
"The elections are a referendum on whether we want to go to Europe or to remain alone ... to live like other European nations or to be isolated in the Balkans," the president said.
Tadic took telephone calls from citizens on Thursday, while Kostunica's DSS prepared to hold their final campaign rally in the same Belgrade square later in the day.
Campaigning comes to an end at midnight on Thursday, before the 6.7 million electorate is given two days to contemplate who they will back ahead of Sunday's vote.