Mr Rasmussen has been a backer of Nato's mission in Afghanistan
The US is prepared to back Danish Prime Minister Anders Fogh Rasmussen to be the next secretary general of Nato, US and alliance sources say.
The current secretary general, Dutch diplomat Jaap de Hoop Scheffer, steps down at the end of July.
Mr Rasmussen, Denmark's premier since 2001, is already reported to have the backing of France, Germany and the UK.
Mr Rasmussen is a strong supporter of Nato's mission in Afghanistan, sending a contingent of 750 Danish troops.
However, he has not confirmed his candidacy and the appointment needs the unanimous backing of all 26 Nato member states.
Turkey is said to have misgivings about Mr Rasmussen over his refusal to apologise for the publication of cartoons in a Danish newspaper in 2005, one of which depicted the Prophet Muhammad with a bomb in his turban.
The cartoons sparked a worldwide controversy.
Traditionally the post of secretary general is usually held by a European while the Nato's military commander is American.
Other contenders for the position include Polish Foreign Minister Radoslaw Sikorski, Norwegian Foreign Minister Jonas Gahr Stoere, former British Defence Secretary Des Browne, former Bulgarian Foreign Minister Solomon Passy and Canadian Defence Minister Peter MacKay.