"Several protocols were ignored," unnamed aeronautical sector sources told online news site El Confidencial.
The computer system that controls the plane's engines, the Full Authority Digital Engine Control (FADEC), "should have been tested before, in a simulator, to check if everything worked," it added.
The sources claimed the protocols were skipped because Airbus was in a hurry to make up for delays in the development and delivery of the A400M military cargo and troop transport plane which is assembled in Seville.
The A400M plane that crashed in a field and burst into flames just north of Seville's airport on May 9 was undergoing a test flight, before it was due to be delivered to Turkey in July.
Two of the six people on board the plane, a mechanic and an engineer, survived the crash and were sent to hospital in critical condition.
A senior Airbus executive said Thursday that analysis of the flight recorders of the A400M indicated there were no structural faults but assembly quality problems.
The units which control the engines of the plane were poorly installed during final assembly, which could have led to the engines malfunctioning,
Airbus group's chief of strategy Marwan Lahoud told the German daily Handelsblatt.
Fabrice Bregier, chief executive of the plane making unit of Airbus Group, said Saturday that was "either a weakness in the test procedure of planes before they fly, or a problem that results from the implementation of these procedures."
Airbus's defence and space division told AFP that it was too early to draw any conclusions.
"We will need the full results of the investigation in order to have the full picture, so as long as there is no further communications from (the investigating authority) CITAAM it is too early to draw any conclusions from the accident," it said in a statement Tuesday.
"Like all accidents, it will certainly be a combination of issues and not one single cause," the company added.