The 34-year-old "Batman Begins" star, who last year divorced Tom Cruise, the father of her daughter Suri, has been growing close to Kirby and their chemistry appears to have taken the next level, reported Contactmusic.
"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," a source said.
"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 source added.