Joe Jonas and Sophie Turner have been embroiled in a bitter, child custody dispute, but they have been spending hours together over the last 2 days trying to hammer out a divorce settlement … multiple sources tell TMZ.

As TMZ reported, Joe and Sophie have a prenup, and one of the provisions is that they go to mediation to settle all outstanding issues related to their divorce … this according to multiple Joe/Sophie sources.

Joe and Sophie spent a full day Wednesday hashing out divorce issues, and we’re told they are dealing with a property settlement guided by the prenup, as well as child custody.

As you know, there’s a jurisdictional dogfight going on over which judge will handle the case — a Miami judge, which is what Joe wants, or a UK judge, which is Sophie’s choice.

Sophie has filed legal docs in federal court trying to get the case removed to the UK. Although there’s an active legal dispute over jurisdiction, our sources say they are trying to reach an agreement on both which judge handles the case and what the custody arrangement should look like.

It appears Sophie wants to live in the UK with the kids and Joe wants them to stay put in the U.S., but they are trying to reach some sort of custody agreement that would make jurisdiction essentially irrelevant.

We’re told they’re both down with joint custody, and if they can agree on a structure — for example, the kids stay with one parent during the school year and the other parent during the summer with both parents getting visitation — they would probably just ask the Florida judge to ratify it.

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The good news … since they’re in mediation, which continues on Thursday, it appears neither Joe nor Sophie are challenging the prenup.

It’s possible they could pull a Kevin Costner and settle the latest, contentious divorce.