On October 16, 2018, the United States Trade Representative (USTR) notified Congress that the Trump administration intends to enter into negotiations for a trade agreement with the E.U. This notification is part of the Trade Promotion Authority process, which requires ongoing consultations with Congress. You can view the notification here
Both parties have the mandate to enter into negotiations. However, there has been no forward movement because there is disagreement between the two parties about what will be negotiated.