The ruling National Resistance Movement is expected to officially nominate Mr Museveni as its candidate later on Friday.
Court appearance?
Earlier this year, the United Kingdom and other donors withheld some aid to Uganda after the constitution was amended to allow Mr Museveni to run for a third term.
On Thursday, the United States called for a fair and speedy trial for Dr Besigye which does not affect the elections.
It said it was "deeply concerned" about his arrest and regretted the two days of riots in the capital, Kampala, that followed.
Dr Besigye may be taken to the High Court on Friday for a bail hearing after not appearing as expected earlier in the week.
The Monitor has carried an advertisement asking people to contribute to a legal defence fund for Dr Besigye but Mr Nkutu said he was not aware of how this could break the law.
The paper and its sister radio station have frequently been criticised by the government and earlier this week, there were reports that the authorities were considering closing the paper down over its reports on the military.
'Trumped up'
On Wednesday, 14 of Dr Besigye's co-accused received bail, but when gunmen in black T-shirts arrived outside the court they refused to leave and returned to prison.
They then stood at the exit to the High Court waiting for treason suspects to leave, our correspondent says.
Officials from Dr Besigye's Forum for Democratic Change (FDC) said it was too dangerous to release the accused to the unknown gunmen.
Opposition onlookers and lawyers were furious, accusing the military of invading the High Court, our correspondent says.
Earlier, Dr Besigye's wife Winnie Banyima, a former MP, told the BBC she thought the charges against her husband were "trumped up" and said he had suffered intimidation since he declared his intention to challenge the president before polls five years ago.
Once Mr Museveni's doctor, Dr Besigye ran against the president in 2001 before fleeing after the elections, saying his life was in danger.
Dr Besigye returned from four years of exile last month to large crowds of cheering supporters.
If found guilty of treason, he and 22 co-accused could face the death penalty.
Dr Besigye has previously denied allegations that he is linked to rebel groups.
The rape charge dates from an incident in 1997, allegedly involving the daughter of a friend.