"Anders Fogh Rasmussen is the strongest contender for the post," the source told a RIA Novosti correspondent.
Rasmussen has rejected media speculation in the past, saying he still has unfinished work in Denmark and was intent on seeking a fourth term as head of government.
The term of NATO Secretary General Jaap de Hoop Scheffer expires on July 31.
Belgium's Le Soir newspaper earlier reported that Poland's Foreign Minister Radek Sikorski, along with the Danish prime minister, who supported the U.S.-led invasion of Iraq and addressed NATO operations in Afghanistan in his New Year speech, were the top candidates to head the military alliance.
Sikorski has also denied he plans to put himself forward for the post of NATO secretary general.
Czech Deputy Prime Minister Aleksander Vondra, Norwegian Defense Minister Anne-Grete Strom-Erichsen, former Bulgarian foreign minister Solomon Passy and two Canadian politicians, Defense Minister Peter MacKay and former deputy premier John Manley are also seen as potential candidates.
