Tom Cruise 'Misses Suri Very Much,' Says a Source

09/21/2012 at 03:45 PM EDT

Suri and Tom Cruise in January 2012

Sharpshooter Images/Splash News Online

Tom Cruise misses his little girl.

The actor, whose divorce from Katie Holmes became official last month, hasn't seen their 6-year-old daughter Suri in over a month but the father and daughter are in constant contact, a source tells PEOPLE.

"Tom talks to Suri several times a day. He misses Suri very much," the source says.

Cruise, 50, has been filming All You Need Is Kill in Europe, where the source says, he has a grueling daily schedule of pre-production work.

Suri, meanwhile, has a busy schedule of her own now that she's in school. The tot started first grade on Sept. 11 in New York City, where she lives with Holmes.

"[Tom and Suri] are very, very close," the source adds. "He's up on everything that's going on in her life."

Cruise and Suri last spent time together during a fun-filled trip to Disney World in early August, which included staying in the Cinderella Castle Suite and frolicking in the waves and Disney's Typhoon Lagoon.