Talks have been held between the Gunners and Beckham's representatives, which would allow the former England captain to use their London Colney training facilities throughout the winter.
He will not be playing any games for Los Angeles Galaxy, and the Sunday Mirror claim that he wants to train close to his Hertfordshire home.
But Beckham will not be pulling on Arsenal's shirts at all, as this would not be a loan more - the Galaxy have ruled out the option of him representing any club other than their own.