The stars were reported to have grown close after auditioning for movie musical Les Miserables, but Redmayne, who landed the role of Marius Pontmercy in Tom Hooper's new film, is adamant the speculation was false.
He reveals Swift once visited him backstage while he was starring in a play, but romance never blossomed.
The actor tells Britain's Glamour magazine, ""It was absolute nonsense. We had a chat behind the stage for seven minutes. Even by my standards, that's a pretty brief relationship!""
Swift was in the running to play Eponine in Les Miserables, but the role eventually went to West End star Samantha Barks.