The 'On the Floor' hitmaker recently split from the 27-year-old dancer after two-and-a-half years of dating and the "generous" singer - who has six-year-old twins Max and Emme with ex-husband Marc Anthony - wanted him to have some lasting mementos from their relationship.
A source said: "He gets to keep all the gifts that Jennifer bought him, including the customised truck that she gave him for his 25th birthday.
"Jennifer has always been very generous and Casper has bags of things to move out."
Over the weekend, Casper was seen moving his belongings out of the 44-year-old star's home and is said to be devastated about the split.
A source told People magazine: "He is upset about the split. He really wanted to stay with Jennifer. He loves her and her kids."
It was recently claimed the 'American Idol' judge is determined to stay friends with the choreographer as her kids have developed a bond with him.
The source explained: "She will definitely still keep things civil and actually still loves him. The hard part is the kids love him too. He has become a part of her family.
"It's not going to be one of those breakups where you never see them together again."
Meanwhile, in recent weeks, Casper has been accused of cheating on the star with transsexual bikini model Sofie Vissa, whom he met and exchanged sexual messages with online first.
However, Casper has denied the allegations and subsequent claims involving a second transgender model.