Katie - who divorced Mr Cruise in August last year after five years of marriage - has apparently enjoyed several dates with the 'Brokeback Mountain' star, including several romantic dinners at Jake's West Village apartment in New York.
We wonder what was on the menu?
The pair have also both been to see each other's Broadway plays - Katie is currently starring in 'Dead Accounts' while Jake is treading the boards in 'If There Is I Haven't Found It Yet'.
According to Grazia magazine, they were introduced by Katie's old 'Dawson's Creek' mucker Joshua Jackson.
"Josh has been the mastermind behind this romance," a source told the mag.
"Katie says that they have tons in common and Jake has already been to see her in Dead Accounts, plus she has been over to his apartment in the West Village for dinner."
Katie's alleged new romance will at least put a smile back on her face after it was announced her play is being pulled after just six weeks on Broadway.
'Dead Accounts' was originally set to run until 24 February but will now end on 6 January after poor ticket sales.
> IN PICS: CELEB LOVE SPLITS 2012