The prize, which was given to the global chemical weapons watchdog on Friday, "should have been mine", Assad said, according to Al-Akhbar newspaper.
Assad made the remark "jokingly", the daily said, as he commented on the award on Friday of Nobel Peace Prize to the Organisation for the Prohibition of Chemical Weapons, which is working in Syria to destroy the Assad regime's massive chemical arsenal by mid-2014.
Al-Akhbar also reported that Assad had proposed in 2003 that all countries in the region should hand over all weapons of mass destruction.
The OPCW and the UN have had a team of 60 experts and support staff in Syria since October 1, while the civil war rages on.
The team started its work after a breakthrough UN Security Council resolution last month ordering Syria's chemical stockpile destroyed.