Jennifer Aniston is near a deal to star in “Object of My Affection,” the Wendy Wasserstein-scripted adaptation of the Stephen McCauley novel, to be directed by Nicholas Hytner. The film, described as a contemporary romantic comedy-drama about the relationship between a straight woman and a gay man, has been set up at Fox and will be shot in New York City beginning in June with a budget a shade below $20 million.“Object of My Affection” is being produced by Laurence Mark, who has been working for several months to set it up. Due to an underlying rights issue, Paramount had first shot at the project, when Keanu Reeves was being considered to play the lead. Par passed, but the project quickly found a home at Fox. Hytner has a strong relationship with Fox president of production Tom Rothman, who made the critically acclaimed “The Crucible” at Fox. Rothman ran Samuel Goldwyn when Hytner directed his breakthrough film “The Madness of King George.” It is unclear whether Reeves will play the male lead. Aniston, next seen in Fox’s August comedy “Picture Perfect,” will make the film on her hiatus from TV’s “Friends.” She’s repped by CAA’s Kevin Huvane and Patrick Whitesell, and managed by Molly Madden of 3 Arts. Hytner just completed direction of the play “The Cripple of Inishmaan” at the National Theatre in London by playwright Martin McDonagh. He’s repped by CAA’s Huvane and Joe Rosenberg.