The 50-year-old actor was seen getting close to the blonde beauty - whose sister is his `Rock Of Ages` co-star Malin Akerman - at the afterparty for the Swedish premiere of his latest movie `Jack Reacher` in Stockholm and are even thought to have left the party together.
A source told The Sun newspaper: "They already knew of each other from Malin being in `Rock Of Ages` so they didn`t need much of an introduction.
"Even though Tom was working the room, once they got chatting they were locked in.
"They seemed very natural in each other`s company for most of the night and at the afterparty at the Rose club. Then all of a sudden they were gone... "
Tom - who has children Isabella, 20, and Conor, 17, from his marriage to Nicole Kidman, as well as Suri, six, with ex-wife Katie Holmes - had to fly to New York afterwards, while Jennifer headed to London but the pair are planning to meet up again in the US very soon.
The source added: "Jennifer lives close to Malin in LA so a meet with Tom before Christmas is more than doable."