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The 34-year-old actress - who divorced Tom Cruise, the father of her seven-year-old daughter Suri, last year - has been growing close her 'Mania Days' co-star in the past few weeks and their blossoming chemistry appears to have moved to the next level.
A source said: "Katie and Luke are getting closer with everyday they spend together - and at the moment, with the filming schedule so tight, that's nearly seven days a week.
"The chemistry between them is tangible but that's all because since their break in filming in July, Katie and Luke have stayed in constant contact. "
The 35-year-old actor is rumoured to have split with his long-term girlfriend Andrea Sarubbi amid speculation about his relationship with Katie, but Luke is said to be in turmoil over the women in his life.
The source explained to LOOK magazine: "Luke is currently trying to figure out his relationship issues with Andrea. I don't think he knows what to do. Katie's trying to be a friend to him, as she would to anyone, but the more time they spend together, the more time they spend together, the more she seems to be falling for him.
"She even jokes he's her Mr. Right - but the elephant in the room in his confusion over what's happening with Andrea."
