The star, who portrays Roosevelt's cousin and companion Daisy Stuckley in new movie Hyde Park on the Hudson, always had her suspicions about her character's ties to the president - and she admits a trip to Stuckley's former home left her in no doubt that the pair was deeply fond of one another.
Linney says, "Most people don't know that she even existed, her name was Daisy Stuckley and she was FDR's cousin and very, very close confidante.
"This woman lived to be 100 years old and she was a real wallflower; no one took her very seriously and she always feigned ignorance to anything about the president - she was just a cousin who helped keep him company.
"When she died, under her bed was a little suitcase filled with letters and diaries that (suggested) their relationship was much more extensive than anyone understood and was non-platonic. I saw the suitcase.
"Her home is this amazing museum... and you can go there and learn all about Daisy and her family... and the letters are all at the presidential library in Hyde Park.
"People were kind enough to let me into her bedroom, which is exactly the way it is when she died and she slept in a single bed and she woke up every morning and the first thing she saw was a huge lithograph of FDR and next to that was a vitrine filled with little knick-knacks, things that he would pick up... the equivalent of stuff you would pick up at airports at the last minute (for a loved one)."