Stormy's attorney, Clark Brewster, tells TMZ ... his client recently received lots of "vitriolic messages" on social media, including some very concerning direct messages.

The alleged threats come on the heels of Trump announcing Saturday he expects to be arrested Tuesday by Manhattan DA Alvin Bragg over the notorious Stormy Daniels hush-money case.

Stormy's attorney says she's taking extra precautions -- her team doesn't want to share specifics, for fear of tipping off someone who might want to do her harm. ... Brewster has only said in the past, "Stormy for years has had security when she needs to."

As for some of the nasty online comments, Stormy's been called a "Worthless Whore," "degenerate prostitute" and an "extortionist who should be in prison."

Remember ... Bragg has been investigating Trump for allegedly making a $130,000 payment to Stormy ahead of the 2016 election. Trump is accused of brokering the deal with the porn star to buy her silence over their alleged affair, accusations Trump has long denied.

Stormy, we're told, has been threatened before over DM ... and her attorney says Stormy knows what steps to take to ensure she's safe and comfortable.