The 'Terminator' actor has reportedly been talking on the phone with Mildred Patricia Baena – who went into hiding following revelations of their affair – and wants to meet up with her and start building a relationship with their son Joseph, 13.
A source told TMZ.com: "Both families are open to a meeting, it just hasn't happened yet."
Since news of the relationship broke in May, Mildred - a former member of the Schwarzenegger family's staff - hasn't been back to their house or her own home in Bakersfield, California.
No his wife Maria Shriver has filed for divorce, Arnold is keen to play an active role in Joseph’s life.
A source told RadarOnline.com: "Arnold wants to spend time with Joseph and play more of an active role in his life. In a way, Arnold is relieved that he no longer has to hide the fact that he is Joseph’s father.”
Arnold and Maria – who have four children together, Katherine, 21, Christina, 19, Patrick, 17, and Christopher, 13 – have entered divorce negotiations, with the latter expected to get a substantial part of her husband's estimated $700 million fortune.
It has been reported former Californian governor Arnold will keep the family home in Brentwood, while Maria is looking to buy a $10 million house nearby.
Further details are still being worked out by divorce lawyers for the couple.