The veteran midfielder has become a free agent after deciding not to renew his contract with LA Galaxy and has been heavily linked with a return to Europe.
Several Premier League clubs, including QPR and West Ham, have expressed interest in his services, but the latest reports suggest AS Monaco is leading the race.
Beckham is expected to make a decision on his future by the end of the month and L’Equipe suggests that Monaco could very well be his next destination.
The French giants are on the verge of returning to the top flight and their wealthy owners believe the arrival of David Beckham could attract more star players to Stade Louis II.
Monaco could offer the English midfielder a six-month deal in the January transfer window or wait until the summer to make sure they gain promotion to Ligue 1.