The 26-year-old actress - who previously had a long-term relationship with DJ Samantha Ronson and has been linked to James Franco - would relish the opportunity to fall in love, but has not found it has happened for her yet.
The troubled actress stars as Elizabeth Taylor in TV movie 'Liz and Dick', about the late star's longstanding love for Richard Burton - whom she married twice - and Lindsay hopes she can find a comparable suitor for herself.
The 'Big Hoops (Bigger The Better)' singer - who has previously appeared on the small screen in 'Roswell' and 'One Life to Live' - will be performing in the episode, which will air in November, E! News reports.
The 25-year-old actress was seen getting cosy with her ex-girlfriend - who she dated for two years from 2007 to 2009 before briefly getting back together last year - at New York nightclub Le Baron earlier this week, and reportedly ''couldn't get enough of each other'' while partying the night away.
Lindsay Lohan has sworn off dating to focus on her career.
The 25-year-old star - who is set to play screen legend Dame Elizabeth Taylor in Lifetime movie 'Liz and Dick', about the actress' love affair with Richard Burton - is keen to avoid any distraction and so will not be pursuing a relationship for the moment.