German Chancellor Angela Merkel, French President Nicolas Sarkozy and British Prime Minister Gordon Brown want Rasmussen to replace Jaap de Hoop Scheffer when he steps down in July, the Süddeutsche Zeitung daily said Saturday.
US President Barack Obama's administration is expected to say whom it favours just ahead of a NATO summit on April 3-4 in Baden-Baden and Kehl, Germany, and in Strasbourg, France, the paper said in its Saturday edition.
Usually the post of NATO secretary general is held by a European while an American, currently General John Craddock, is supreme allied commander Europe, the paper said.
Rasmussen, 56, supported the 2003 US-led invasion of Iraq and favours a strong NATO involvement in Afghanistan, it said.
Seen as a strong candidate for some time, he has been touring European capitals drumming up support in recent weeks, and is due to meet James Jones, Obama's national security advisor, before the April summit, the paper added.
A spokesman for the German government said NATO member countries were still in talks over the appointment and that no decisions had been taken.