"This has been called the real-life War of the Roses," Jon's attorney Mark Heller told People, "and he brought that as a peace offering to break the ice and try to bring the war to an end."
But Kate, also present at the daylong divorce arbitration hearing on Saturday, turned them down.
According to Heller, the arbitrator is expected to rule in a month, and the divorce could be finalized by the end of the year.
During the arbitration, custody, child support and distribution of assets were addressed.
"There were a couple of very emotional moments," said Heller, "but in the end it all came together and concluded on a happy note."
Monday marks the finale of TLC's Jon & Kate Plus 8.