The actress is said to have been offered a "megabucks" deal to appear on the Channel 5 reality show, on condition that US courts allow her to leave the country.
Producers have flown to LA to negotiate with the Mean Girls star and have even shot background footage of her for use in the show when it returns in January, the Sunday Mirror reports.
Lohan spent four-and-a-half hours in an LA jail last month after failing to complete court-ordered community service. She has a month of community service to complete at a Californian morgue, but is apparently ahead of schedule.
TV bosses will do "everything possible" to get her in the house and hope to persuade the courts to allow Lohan to leave the country by arguing that Celebrity Big Brother will help get her life back on track.
"Lindsay would be an absolutely amazing signing for us," a source said. "She's a Hollywood A-lister and everyone knows about all the trouble she's been in.
"She's a fiery character too, so there are sure to be some major clashes with other celebs if we get her in the house.
"We want this to be the best Big Brother ever. So we hope that the courts will make a special allowance in this case. There aren't many more controlled environments than the Big Brother house."
It was recently reported that Lohan had signed a $1m deal to pose nude in Playboy magazine. Her latest jail sentence was reportedly delayed to allow time for the shoot.
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