The divorce came final this month and Penn, who is in Dublin to film a new movie called 'This Must be the Place,' will turn 50 while there.
He and Wright will share custody of their 16-year-old son Hopper; they also have a 19-year-old daughter, Dylan.
A source told The Evening Herald he is truly enjoying his Irish stint.
"He's here to work and takes every project very seriously, but he's also hoping to have a bit of free time to go to some museums or art galleries while he's here and get a real taste of culture," said an insider.
"He's also looking to mark his 50th birthday in a unique way while he's here in Ireland."
Filming on his the new movie will start on August 16. Co-stars include fellow Academy Award-winner Frances McDormand.
Penn, plays an aging rock star pursuing a Nazi criminal who killed his father is in a concentration camp.
His character is called Cheyenne, a man who lives a quiet life in Dublin with his wife, played by McDormand.
When his father, a holocaust survivor, passes away in New York, he embarks on a journey to track down his father's nemesis.