The terms of the deal have not been disclosed. But according to US website TMZ, prosecutors want Lindsay to plead guilty and serve six months instead of going to trial where, if convicted, she would potentially face a longer sentence.
Lindsay was reportedly hoping she would avoid time behind bars following a two week stay in jail last summer after a violation of her probation on a previous drink-driving conviction.
Speaking in court on Wednesday, Judge Schwartz said he doubted the Mean Girls star would take the deal.
"I get the impression you are not going to accept the (prosecutors') offer, okay," he said. "I don’t have a crystal ball, and I'm not privy to any inside information, but that is the feeling I got."
The judge warned her sternly that "this case does involve jail time. Period. If this case is resolved in front of me – you are going to jail.
"Now, there may be an issue as to the amount of time that you go for and that's why a judge has discretion in sentencing.
"But if it settles here, I don’t want you under any misapprehension, you will be going to jail, period."
He also told the star not to expect any special treatment.
"I never met you before the last court appearance, you never met me," he said. "One of the things about me is that I treat everyone the same. I don’t care you are Lindsay Lohan versus John Doe or Jane Doe."
Lindsay - dressed demurely in cream trousers, a Chanel top and high heels and with her hair tied back in a ponytail - was accompanied at the 8.30am hearing by her mother Dina and her younger brother.
Her father Michael was also there and he spoke outside court to show his support.