The 35-year-old Alfie actor and the 20-year-old model first sparked rumours of a romance when they attended a Radiohead concert together last month in London.
They reportedly attended the theatre together at a later date and were spotted having dinner together in Covent Garden.
A source to the Sunday Mirror said: "Jude was keeping low-key. They were deep in conversation and making each other laugh."
"There was no blatant kissing but it was obvious they were more than just friends. Jude was being very affectionate and gazing into her eyes."
Jude Law was previously engaged to Alfie co-star Sienna Miller in 2005, before their relationship broke down after Jude cheated on the actress with Jude's Nanny at the time Daisy Wright.
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