Al Jazeera's Alan Fisher, reporting from Downing Street, said there had been an air of expectancy that Brown may step down, with the Liberal Democrats previously making it clear they were not willing to work with the prime mnister.
But he said "clearly Brown isn't ready to pack the bags yet and leave Downing Street".
Uncertainty over who will be the next prime minister is high, after Thursday's vote resulted in a tight race with no clear majority.
So far the Conservatives are in the lead with 301 seats, 25 short of the 326 needed to make a parliamentary majority. Labour are trailing them on 255.
Earlier, Nick Clegg, leader of the Liberal Democrats, appeared to back the opposition Conservatives right to attempt to form a government.
"I think it's now for the Conservative party to prove that it is capable of seeking to govern in the national interest," he said on Friday morning.
David Cameron, the leader of the Conservatives, has said that the Labour party had "lost its mandate" to rule.
"I believe it is already clear that the Labour government has lost its mandate to govern our country," Cameron said.
Ruth Fox, the director of the government and parliament programme at the Hansard Society, said that she expected to see the uncertainty resolved soon.
"I would expect over the weekend and definitely by Monday to have some sort of resolution," she told Al Jazeera. "Given Nick Clegg's statement today we might get something earlier than that."
While there was no clear winner, the election did throw up some interesting results, including the first ever seat for the Green party, represented by Caroline Lucas in Brighton Pavillion.
Two former Labour interior ministers, Jacqui Smith in Redditch and Charles Clarke in Norwich South, lost their seats.
The far-right British National Party failed to make headway in Barking, with Margaret Hodge, the sitting Labour MP, increasing her majority.
Voters turned away
Voters in some British districts reported that they were turned away from polling stations after large queues formed shortly before polls closed at 21:00 GMT.
Britain's electoral commission said on Friday that challenges to some national election results were likely as a result and that they had launched an investigation.
|Liberal Democrat leader Nick Clegg has said he will act in the national interest [Reuters]
Problems with people being unable to vote were reported in areas including Milton Keynes in southern England, in Sheffield, the city where Nick Clegg, the Liberal Democrat leader holds a seat and Newcastle in northern England.
Police were called in London to one demonstration where 50 people refused to leave a polling centre after officials told them they were too late to vote.
Speaking to Al Jazeera, Daniel Hamilton from Comres, a polling organisation, said:
"It's very concerning and I think there's a growing sense of anger among all political parties across the country that there is a feeling that some people, notably in some key marginal seats, appear to have been almost disenfranchised.
"I think whatever happens, whoever forms the government, there will be an urgent inquiry called by the leaders of all the three main political parties.
"For there to be an investigation into why this happened and how this appalling situation can be avoided in the future."
The failure of the election to produce a clear result is likely to keep financial markets under pressure due to concerns about uncertainty over who will form the next government.