But Rasmussen's candidacy has been met with opposition from Turkey, which voiced anger at his handling of a row over cartoons in a Danish newspaper depicting the Prophet Muhammad.
Recep Tayyip Erdogan, Turkey's prime minister, told Al Jazeera's Frost Over The World on Friday that Rasmussen would "not be elected if Turkey has a negative approach".
"We are receiving telephone calls from the Islamic world, telling us: 'By God, this person should not become the secretary general of Nato and we have to take into consideration all these reactions'."
Turkey has suggested it could veto the nomination of Rasmussen, who has been tipped as the favourite to succeed de Hoop Scheffer when he steps down on 31 July.
The Turkish prime minister, speaking at a conference in London earlier on Friday, said Rasmussen failed to act on Turkish requests to ban a Denmark-based TV station linked to Kurdish rebels, and criticised his stance during the row over the controversial Danish cartoons.
"How can those who have failed to contribute to peace, contribute to peace in the future? We have doubts ... and my personal opinion is negative," he said.
The military alliance is expected to announce a successor during its two-day summit in Strasbourg, which ends on Saturday.
A spokeswoman for Rasmussen said on Friday that the Danish leader told his party colleagues he was a candidate for the role.
Opposition to candidacy
The Danish prime minister had denied running for the post until three weeks ago, when he refused to comment further.
Erdogan said last week that Rasmussen would be unwelcome as Nato's chief.
The Turkish prime minister said he had received calls from the leaders of Islamic countries urging Turkey to veto the Danish prime minister.
Rasmussen infuriated some Muslims by speaking out in favour of
freedom of speech during a row over the publication of cartoons featuring caricatures of the Prophet Muhammad in the Jyllands Posten newspaper in 2006.
Ankara has also criticised Denmark for failing to revoke the broadcasting licence of a Kurdish television station, which Turkey says is a mouthpiece for the Kurdistan Workers' Party (PKK), an armed group which is fighting the Turkish government.
He has also angered Turkey by opposing its membership in the European Union (EU).