Russell Brand is planning to appeal his conviction for raping and sexually assaulting 3 victims in the United Kingdom, TMZ has learned.

Multiple sources tell TMZ ... Russell's lawyers are "drawing up" legal papers to appeal the criminal conviction that's sending the actor-comedian to prison for more than a decade. We're told the appeal has not yet been filed, but Russell's lawyers began talking about an appeal last week.

As you know ... On Monday, the judge delivered Russell's stiff sentence -- 10 years and 6 months -- in London's Southwark Crown Court with Brand and his wife Laura looking on.

After a 4-week trial, the jury found Russell guilty of one count of rape and three counts of sexual assault. Just before sentencing Brand, the judge slammed Russell for his horrible treatment of his three victims.