Brad Pitt and Neri Oxman have reportedly been talking on the phone "several times a day".
The 54-year-old actor has recently been linked to the 42-year-old Massachusetts Institute of Technology (MIT) professor, with claims they've been dating for six months.
A source told Us Weekly magazine: "They continue to talk on the phone several times a day and are very infatuated with each other.
"Their busy schedules are going to be a huge challenge because Neri isn't going to give up her life in Cambridge or her job at MIT for anyone, even Brad Pitt."
While it's said the couple "are going to have fun" and see what happens, it's reported that Neri may struggle with their romance coming under the spotlight.
The insider added: "Neri is extremely uncomfortable with all of the media attention and feels that her personal life has now come under a microscope.
"Brad feels badly about this of course, but he is powerless to stop it."
It comes after the 'World War Z' actor split from his estranged wife Angelina Jolie - with whom he has Maddox, 16, Pax, 14, Zahara, 13, Shiloh, 11, and nine-year-old twins Knox and Vivienne - in September 2016 after two years of marriage and almost a decade of dating.
Although their split was a "sad" time for the actor, he is now reportedly feeling happier than ever.
A source said: "Separating was very sad and shocking to him, but he started taking care of himself again. He seems much, much happier."
Brad's newfound happiness also comes after it was reported he had made several changes to his lifestyle since becoming a single man.
Another source said: "He has made changes in his life since the split.
"When they first split he spent a lot of time at home and was often very down about what was going on. He was a homebody for many months, but in the last month or two, he's been going out more. He enjoys going out to eat with close friends."