Clunes had previously appeared as a guest on the show
The makers of BBC One's satirical news quiz Have I Got News For You have denied reports that ratings winner Martin Clunes is to become the show's full-time host.
Clunes, who was the guest presenter for the first show of the new series, was said to have been offered the job, according to tabloid reports on Tuesday.
Last week's show, hosted by the former Men Behaving Badly star, attracted 9.5 million viewers for each of its broadcasts on Friday and Saturday.
The show had six million viewers when Angus was hosting it, and we have been getting over seven million since he left
But a spokeswoman for the BBC said that despite Clunes being "superb" on last week's show, they had not offered him a permanent position.
The actor has been one of a number of guests hosting the topical satire after presenter Angus Deayton was sacked last year following tabloid allegations about his private life. He had been with the show since the first series in 1990.
This week the show will be presented by former Tory leader William Hague, and teenage singer Charlotte Church will front it the week after.
The spokeswoman said the programme was looking for a permanent host, but it was "not a decision we're going to be rushed into".
Paul Merton won a Bafta this month for his part in the show
"Angus was never removed from the show because of his ratings, but it had six million viewers when he was hosting it, and we have been getting over seven million since he left," she said.
The programme's makers, Hat Trick, had not made an offer of a permanent position to anyone since Deayton's departure, she said.
Past guest presenters included broadcaster Anne Robinson, political journalist John Sergeant, and Tory MP and Spectator editor Boris Johnson.
'A dull man'
Comedian Paul Merton, one of the team captains alongside Private Eye editor Ian Hislop, also presented one show.
Earlier this month he said Deayton was "a dull man", that his loss was "not a big deal" and that producers were right to sack him.
At the end of 2002, a hint to the type of permanent successor being sought was given by Jimmy Mulville, joint managing director of Hat Trick.
"It won't be a complete unknown," he told a newspaper.
"But it may be a journalist whom we all know but who hasn't done TV before, or an actor who is not an A-lister."
Comedian Alexander Armstrong, one half of duo Armstrong and Miller, is reported to be among the favourites.