Ideally it would be nuclear powered, but practically it's not happening. Building a BBGN would preempt building a CV.
The US would need to re-certify Pascagoula as a nuclear shipyard, or rebuild one of the former shipyards in California.
CNO Adm Caudle stated the BB won't be nuclear powered as wanted ship in the water ASAP, if true for nuclear it should also rule out IEP as its even slower in build time, it took BIW just under 10 years before shipping the Zumwalt Lyndon B Johnson to Ingalls, Pascagoula for the installation, activation and testing of its combat system. BIW steel was first cut April 2012 and it arrived at Pascagoula January 2012, still yet to be commissioned.
Presume that only leaves GTs and/or Diesels and maybe Electric Motors? Understand the Japanese ~17,000 ton ASEV cruiser is GT and Diesel.
US Navy leaders embrace Trump-class battleships
U.S. Navy leaders speaking at a military conference outlined what they described as the strategic opportunities of the recently announced battleships.