The former Indian foreign secretary, Salman Haider, was the front-runner to head the new UN mission in Iraq, diplomats said on Friday.
No decision has yet been made although one was expected shortly, associate spokesman Stephane Dujarric said.
Annan was to have chosen a special representative by Friday but the announcement was delayed because of his travels. Diplomats also said some candidates had refused because of the precarious safety situation in Iraq.
As a frequent commentator on international affairs, Haider was critical of the US-led invasion of Iraq. Haider, a Cambridge-educated Muslim, was India's foreign secretary from 1995 to 1997, a post equivalent to a deputy foreign minister.
He served briefly as India's high commissioner, or ambassador, to Britain in 1998 before retiring from the diplomatic service.
The diplomats gave credence to Haider's candidacy after he was interviewed by Annan in Qatar last week and came to UN headquarters in New York this week.
"He is a leading candidate," said Romanian Ambassador Ioan Motoc, this month's council president.
Other candidates mentioned were Surin Pitsuwan, Thailand's foreign minister from 1997 to 2001, also a Muslim, and Ashram Jhansi Ai, Pakistan's ambassador to the United States.
The post has been empty since August 19, when a bomb blast at UN headquarters in Baghdad killed special representative Sergio Vieira de Mello and 21 other people. Annan pulled out all international staff in October after a series of attacks on foreign relief organisations.
A special UN force was expected to guard UN staff, with diplomats saying fresh troops were expected from Nepal, Georgia, Ukraine and Azerbaijan. But Annan and other officials have made clear the UN operation would be a small one.
Senior officials have commuted to Baghdad since foreign staff was withdrawn. Special adviser Lakhdar Brahimi, who for months has said he was not interested in the post, helped form the interim government that took power on June 28. UN elections chief Carina Perelli has also spent considerable time in Baghdad.
"We want to respond constructively, but we do not want to scatter staff around the country if they are going to be vulnerable to hostage-taking or worse," said Shashi Tharoor, the under-secretary-general for public information. "We will help to the extent that circumstances permit".