Uma Thurman believes she and Arpad Busson can reach a "fair" custody agreement.

In a statement, a spokesperson for the 'Kill Bill' star said: "It is unfortunate that this very private discussion regarding Mr. Busson's visitation rights and his participation in decision making has been made public.

"However, we are optimistic that a fair agreement for both sides will be reached out of court."

Uma got engaged to Arpad, who also has two sons, Flynn, 16, and Cy, 11, with supermodel Elle Macpherson, for the second time in 2011 after calling off their first engagement in 2009, but they ended their relationship for good last April.

The actress, who also has daughter Maya, 16, and son Levon, 12, with ex-husband Ethan Hawke, has since been linked to director Quentin Tarantino.

Earlier this year, the star claimed she was happier than she had been in a long time.

She said: "I'm happier now than I've been in many, many years. I'm trying to live as peaceful a personal life as possible. I guess I'm less jaded now than I've ever been, definitely less than when I was younger."