According to E! News, both Lohan, 25, and Fox, 25, are in talks to play the late Elizabeth Taylor in Lifetime's Liz and Dick. (Taylor died of congestive heart failure at age 79 in March 2011.)
"It's a very serious selection," Thompson adds. "It's like casting for Hollywood royalty."
Fox may have an edge over Lohan, as the Mean Girls star is still on probation until the end of March -- provided she complies with the terms of her sentencing.
Liz and Dick will begin shooting in Canada sometime this spring.
Tell Us: Which star would you rather see portray Elizabeth Taylor?