The Spurs shot-stopper has fallen down the pecking order at White Hart Lane, and the report claims he's eager to play first-team football.
The 39-year-old finds his path blocked by France international Hugo Lloris, while Brad Friedel and Heurelho Gomes also compete for first-team action.
Former-Aston Villa keeper Friedel was unseated as Tottenham's number one by Lloris earlier this season, and Cudicini and Gomes have not had a look-in under Andre Villas-Boas.
The Brazilian shot-stopper is reportedly wanted by a number of clubs in Brazil, but his high wages and £3.5m-valuation is putting off potential suitors.
Friedel has also been linked with a move away from Tottenham, with his former club Blackburn Rovers thought to be considering a bid for the 41-year-old keeper.
LA Galaxy currently have Josh Saunders in goal, but following the departure of David Beckham, are believed to be looking to bring in a bigger name.
Cudicini joined Spurs in 2009 from Chelsea, but the Italian has found first-team opportunities hard to come by, and has largely played a bit-part role in the Tottenham squad.