Manfred Weber is due to meet Prime Minister Theresa May on Wednesday. In a video message, he said Britain needs to resolve issues including its outstanding commitments to the EU, because "when somebody is leaving a club" they must pay their bills.
EU leaders say lack of progress on divorce terms is preventing talks from progressing to future relations. They are due to decide next month whether there has been sufficient progress.
Weber, who heads the parliament's center-right EPP group, said on Tuesday that "it doesn't look like" talks will be able to move on in December.