Lin can't do the movie -- for now at least -- because he'll be shooting the sixth "Fast and Furious" movie for Universal. That movie is scheduled to be released May 24, 2013.
An individual familiar with the project told TheWrap Tuesday that Lin never was officially attached, but he was definitely interested in it.
Lin has directed three of the five "Fast and Furious" movies -- the 2006 "The Fast and the Furious: Tokyo Drift," the 2009 "Fast & Furious" and this year's $609.8 million phenomenon "Fast Five."
He's not about to jump off that train. Another reason he's staying on board: "Fast Five" is really important to Universal, and Lin has a production deal there.
It's unclear exactly where the "Terminator" project stands and when it will shoot. Arnold Schwarzenegger was set to resurrect his role as the Terminator, but in May, the former governor put all projects on hold while he dealt with the fallout from a love child he fathered with his housekeeper.
Since then, he and his wife, Maria Shriver, have filed for divorce.
He's now set to play Trench in the 2012 "The Expendables 2," but it's unclear if he'll be back in "Terminator 5."
His spokesman did not return a request for comment Tuesday.
Megan Ellison's Annapurna Pictures acquired rights to the "Terminator" franchise after a bidding war at this year's Cannes Film Festival.
If the project doesn't go into production by 2018, rights revert to James Cameron, who wrote and directed the 1984 "The Terminator."
Deadline first reported the news.