According to some reports, the Iraqi-born architect has already agreed to draw up plans for an Islamic museum in the war-torn capital.
However, although the prospect of designing a building in the country of her birth clearly appeals to her, Hadid has tried to dismiss the claims.
A spokesman for Hadid said: 'She is not sure where the rumours have come from. She has admitted she would quite like to do something in Baghdad, but the stories of an appointment are untrue.'
It is now understood Hadid has written to The Art Newspaper - one of the key sources of the rumour - in an effort to set the record straight.
But broadcaster Dan Cruickshank, who visited Baghdad after the end of hostilities, said that the rumours had a 'certain ring of truth' about them. 'The story has a lovely symmetry and I have nothing against Zaha,' he said. 'But the museum hasn't even been damaged by the war. There's nothing wrong with it.'
He insisted that there are far more pressing issues for both the museum and the city. 'Building a new museum is patently absurd in the current climate. It's a smokescreen to divert attention away from the more important issues. Openness about what was stolen is needed. Security is the priority and if the money is there, what about spending it on protecting the site from looters? The museum building is the least of the worries.'
In April 2003, the world was shocked when news filtered through from the Middle East that the museum was being ransacked by civilians - souvenir hunters keen to lay their hands on historical treasures.