Both Cruise, 50, and Holmes, 33, are said to be keen to avoid the case coming to court and their lawyers have been negotiating privately behind closed doors for several days.
However, the Hollywood star is said to "not want his family dragged through the mud." He may now be open to the idea of the girl living mostly with Holmes in New York. Cruise also has homes in the city and would want wide visitation rights.
In addition to the issues of custody and child support lawyers have also been discussing a property settlement.
Cruise is Hollywood's highest paid star, earning $75 million (£48 million) over the last year, but the settlement is not likely to figure in lists of the largest divorce pay outs.
The couple signed a cast iron prenuptial agreement when they married five years ago, and Holmes is said to be keen to earn her own money from her acting career.
