It's not the first time Park has held out the possibility of a summit, but senior government officials admit the chances of such a meeting are remote given the difficulty the Koreas have in organising talks at any level.
Park's remarks at a New Year press conference followed an address last week by Kim in which he also hinted at a summit - saying he was open to the "highest-level" talks with the South.
"I can meet just about anyone necessary to open the path towards peaceful re-unification," she added.
But Park stressed that the first priority was for North Korea to respond to Seoul's latest proposal - made last month - to resume a high-level dialogue.
"The North should come forward to the talks proactively," she said.
Despite Park's talk of "no pre-conditions" Seoul has repeatedly insisted that any substantive dialogue would require Pyongyang to show some tangible commitment to denuclearisation.
The two Koreas have only held two leadership summits, with the South's late liberal presidents, Kim Dae-Jung and Roh Moo-Hyun, travelling to the North in 2000 and 2007 respectively.
Since succeeding his father, Kim Jong-Un has presided over North Korea's third - and largest - nuclear test, as well as a successful satellite launch.
Noting that North Korea had made "no progress" towards denuclearisation, Park said Pyongyang's nuclear weapons programme continued to overshadow any effort to ease tensions.
"The denuclearisation issue has remained unresolved for long... We can't talk about peaceful reunification while leaving the issue unresolved," Park said.
The North offered Saturday to "temporarily" suspend any future nuclear tests if the US cancelled its annual joint drills with South Korea this year.