Lee, who has split from his 31-year-old wife Liz Kemp, 31, after two years, is determined to give as much of his time to his little son.
Liz, a former Double Bay podiatrist, pulled stumps on the couple's two-year marriage last month.
A cricket insider, who did not want to be named, said: "Brett's focus is completely on Preston now. He wants to be the best dad possible for that little boy. He wants to spend as much time as possible with him. He is the brightest thing in his life right now."
Custody arrangements will take into account the lifestyle of an international cricketer.
Lee said last week that he is available for the forthcoming Tests in India, which would take him away from his son for more than five weeks.
Former Test cricketer now sports commentator Brendon Julian, a father of two young children, was quoted by the Sun-Herald as saying: "Taking on a tour of India is very difficult at the best of times but with the situation Brett faces now it will be even more difficult."
"It will be a testing time both on and off the field. He is a pretty experienced campaigner so when he crosses the line his focus will be on the team but when he comes off his attention will be on Preston," he added.
"A tour of India is not easy even for a married man with kids. I know he is devoted to his family. He has a really good network of family and friends who will support him through this," Julian said.