Paul Manafort’s defense team held talks with prosecutors to resolve a second set of charges against the former Trump campaign chairman before he was convicted last week, but they didn’t reach a deal, and the two sides are now moving closer to a second trial next month, according to people familiar with the matter.

The plea discussions occurred as a Virginia jury was spending four days deliberating tax and bank fraud charges against Mr. Manafort, the people said. That jury convicted him on eight counts and deadlocked on 10...