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The American outfit are said to have laid a deal on the table that would see the Barça star earn around €32m-per-year after tax, according to El Mundo Deportivo.
That staggering contract would be split down the middle with Ronladinho having a €16m playing contract as well as receiving a further €16m for image rights.
After making a profit on the capture of Beckham from Real Madrid, the Galaxy hierarchy believe that they could also do the same with the Blaugrana's fallen idol.
Barcelona are open to the plan after the MLS side also put a bid of €26m to them before going on to outline the deal to the player's brother and agent, Roberto de Assis.
Galaxy look set to be left disappointed though in the same way that Manchester City may fail with their quest to take the player to the Premier League.
Ronaldinho's representatives have made it clear that at 28, the player still believes that he can perform at the top level in European football and is holding out for a Champions League team.
Chelsea are said to be considering a move with new coach Luiz Felipe Scolari to decide after Euro 2008, while AC Milan are still in contact despite them cooling their interest recently.
While Ronaldinho remains in Brazil on holiday, there is also the outside chance that he could remain with Barcelona after lengthy talks with incoming boss Pep Guardiola having taken place.
Lucas Brown, Goal.com