People magazine reported that the estranged couple would prefer to come to an agreement privately and avoid a public battle.
A source explained, "Neither one of them wants this to be hashed out in public."
Holmes was spotted visiting her attorney's office in New York on Friday, however People claims that lawyers for both Cruise and Holmes had been negotiating for several days.
Another insider noted that Cruise "doesn't want his family dragged through the mud. They both love their daughter."
Suri is reportedly the critical issue in their case as Katie filed for sole custody and wants to bring their daughter up in New York. While insiders claim Cruise is receptive to Katie's request that Suri lives primarily with her, any agreement would have to include "generous visitation" for him.
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