* Bidders can still fine-tune offers - sources (Adds fund manager, updates shares): FRANKFURT/DUESSELDORF, Germany (Reuters) - Thyssenkrupp (TKAG.DE) is nearing a full sale of its elevator division, three people familiar with the matter said, adding this would secure the highest valuation of about 16 billion euros ($17.3 billion) to help it pay down debt. The sale, potentially Europe’s biggest private equity transaction in 13 years, is entering its final stretch, with two buyout consortia in a neck-and-neck race to acquire the world’s fourth-largest lift maker.