The 27-year-old actress - who was a guest host on Chelsea Handler's late night talk show 'Chelsea Lately' on Monday night - has been offered more work since her rehab stint, this time on the popular NBC show which she has hosted five times previously.
A source told gossip website RadarOnline.com: "'Saturday Night Live' has approached Lindsay to host the show again, and they were talking about the season opener."
Lindsay is keen to think about the offer as she is a fan of the American comedy show.
The source explained: "She is definitely considering doing it. She loves the show and the people involved."
The troubled star, who recently completed a 90-day court-ordered rehab for substance abuse at the Cliffside Malibu treatment center in California, is coping well since she left the clinic.
The source added: "Lindsay is doing really, really well. She is going to business meetings and she's been on time for every single one of them. This is the best I've seen her in years."
Lindsay has thrown herself back into work since her substance abuse treatment ended, filming a cameo for sitcom 'Eastbound & Down' and appearing on Oprah Winfrey's show.
She is also wanted for a comedy series being developed by Danny McBride for HBO.