Hepburn: Known as the first lady of American cinema
A relative said the 94-year-old actress was suffering from a minor infection.
The Hollywood star was admitted to Hartford hospital in Connecticut on Wednesday for an undisclosed condition.
"She's doing much better today," Ellsworth Grant, Hepburn's brother-in-law, told the Hartford Courant newspaper on Thursday.
The actress's past health problems include arthritis, pneumonia and Parkinson's-like tremors.
Hartford hospital spokesman James Battaglio said on Thursday: "She's up and around and speaking with her physicians.
"Physically she's showing improvement in her overall appearance and her spirit."
He said if Hepburn's improvement continues, she may be released in the next two or three days.
Achievement
Hepburn, who lives in Old Saybrook, near Hartford, her native town, was taken to the hospital after being seen by her own doctor at a clinic in the town.
On Wednesday Battaglio said: "There is no cause for alarm. She is comfortable and stable."
During her 60-year career, Hepburn was nominated for Academy Awards a record 12 times - an achievement equalled only by Meryl Streep.
She has won Oscars for Morning Glory (1933), Guess Who's Coming to Dinner (1967), A Lion in Winter (1968) and On Golden Pond (1981).
Her last film was Love Affair in 1994.
In a rare interview to a New York newspaper last year, Hepburn denied occasional rumours that her health was failing and that she was bed-ridden.
"I am OK", she told the New York Post, adding: "Tell everyone I am doing fine."
She said she was still a big eater and enjoyed home-made meals prepared by her cook.
In her early films Hepburn often portrayed strong female characters.
She won the first of her Oscars at the age of 24 in her third picture, Morning Glory.
Her forthright style has lent itself equally to drama and comedy, and she starred opposite Cary Grant in the 1930s screwball comedy, Bringing Up Baby.
She won an unprecedented fourth Oscar for her performance in On Golden Pond, a remarkable portrait of a resolute woman growing old with grace and grit.