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According to the New York Post, the singer has been involved with Hudson for a year, despite his supposed romance with Jessica Biel.
They were reportedly seen kissing at a Hollywood nightclub last month while Biel was shooting her latest movie in London.
A source told the newspaper: "Kate is very private and refuses to be seen with him in public. She doesn't want to be humiliated like Cameron Diaz was when he dumped her. But they talk every day on the phone and see each other often."
Celebrity website X17online has also claimed that Hudson has been spending time with ex-boyfriend Owen Wilson.
Representatives for both Hudson and Timberlake have denied rumours of a relationship.
