Lee Hee-Beom, head of the 2018 Olympic organising committee, said they had long been preparing for the North's attendance at what he described as the "largest-ever winter festival in history".
"We're making preparations in case North Korea sends not only its athletes but a cheering squad and support staff as well," Lee said.
"The International Olympic Committee has also said several times that it would support North Korea's participation," Lee added.
Kim also announced the reopening of a hotline with the South to discuss attending the Olympics, as a "significant first step" in improving ties.
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Seoul and organisers have billed the Winter Games as a "peace Olympics" and have been keen for the North to take part.
But the main venues are just 80 kilometres (50 miles) from the heavily fortified border and the build-up to the event has been overshadowed by high tensions over the North's nuclear and missile tests.
Choi said he had made the offer to a North Korean official, who reacted positively and promised to convey it to leader Kim.
"A cruise ship will be a convenient solution to the problems with security and lodging," the governor said.
When the North attended the 2002 Asian Games in the South's port city of Busan, its delegation arrived on a cruise ship and used it as a floating hotel during the event.