We got Simpson's longtime attorney Malcolm LaVergne Tuesday on "TMZ Live," and he opened up about O.J.'s finances following his death last week. As Malcolm put it, O.J. died with less than 5-figures in one Nevada bank account, and overall ... had less than millions to his name.

In his final days, O.J. was receiving the maximum amount of social security, as well as pensions from his time as an NFL star and actor. Malcolm claims those payments totaled less than the $400K per year that's been reported.

Mind you, he's not saying Simpson was broke, by any stretch, and admits he lived well during his post-prison life in Nevada.

He says there's signed memorabilia in Simpson's home that can be sold off -- "One man's garbage is another man's treasure. Maybe some people will say, look, even though this means nothing to me ... some guy who is fascinated with O.J. and has a lot of money will pay $50 thousand for it.'"

As we reported, Malcolm's also dramatically changed his tune when it comes to dealing with Fred Goldman, Ron's father. Despite previously declaring the Goldmans would get nothing from O.J.'s estate -- he now says he's happy to meet with Fred, and to pay whatever the law requires.

Remember, the Goldman and Brown families won a 1997 wrongful death lawsuit against O.J., and though they were awarded $33.5 million back then ... with interest, it's now ballooned to more than $100 million.

Malcolm -- who served as O.J.'s attorney before becoming executor of his estate -- acknowledged Fred has a valid claim, and said he plans to reach out in coming weeks to show him what's financially available.