The 37-year-old actress extended the offer to the 26-year-old singer in an interview with Access Hollywood. Rihanna visited Washington, D.C., earlier this week, and posted several photos of herself as Washington's character, Olivia Pope, on Instagram.
"My hope is that Rih, when you're in LA next, you need to come to [our studio], so we can take you on set and we can recreate these photos on our set," the actress said.
Scandal debuted on ABC in April 2012, and is currently in its third season. The series centers on crisis management expert Olivia (Washington) as she navigates her often-complicated personal and professional life.
Katie Lowes and Guillermo Diaz co-star as Gladiators Quinn Perkins and Huck, with Darby Stanchfield as now-White House press secretary Abby Whelan, Tony Goldwyn as President Fitzgerald Grant, Scott Foley as Jack Ballard and Joe Morton as Rowan "Eli" Pope.
Washington's outfits as Olivia inspired a 42-piece capsule collection released at The Limited in September. The actress announced a spring collection for February in the interview, and said the line will include pieces inspired by Quinn, Abby and Mellie Grant (Bellamy Young).
Scandal airs Thursdays at 9 p.m. ET on ABC. Khandi Alexander is slated to return as Olivia's mother, Maya Lewis, on the mid-season finale Nov. 20.