The 70-year-old actor currently has the silkscreen portrait of Farrah hanging above his bed even though the actress - who lost her battle with cancer in June 2009 - left specific instructions in her will that it should be donated to the University of Texas, where she studied before finding fame, along with a second artwork.
The university has now hired an investigator to establish the location of The Missing artwork, according to America's Star magazine.
The Warhol portrait of Farrah was spotted in Ryan's house by viewers of his new reality show 'Ryan and Tatum: The O'Neals', while daughter Tatum - his adult child from a previous relationship - mentions it in her new book 'Found: A Daughter's Journey Home'.
She wrote: "On every wall, there are pictures of us and the rest of the family in our golden days. The original poster from 'Paper Moon', Andy Warhol's portrait of Farrah."
However, Ryan - who has one son Redmond with Farrah - has claimed "all of Farrah's wishes expressed in her will have been fulfilled".
Ryan has previously revealed he feels closer to Farrah when surrounded by her possessions.
He said: "You know, Farrah was a very strong presence in my life. So strong. She permeated my mind and my being. She still does. She had that kind of hold on me. I live in the same house that we lived in together.
"The things that are nice in my house are the things that she got me. And so I hear songs that we loved and it stabs me and brings her back. And I'm OK with that. I had somebody. I had somebody that I loved. OK."