King's has been collaborating with Technische UniversitÃ¤t Dresden on a research initiative, known as Transcampus, since 2015.
But, according to Times Higher Education, an "offshore King's College Europe" is now on the cards.
King's College confirmed that it was discussing potential further collaborations with TU Dresden.
The two institutions already offer 10 joint professorships and several joint PhD programmes through Transcampus.
However, its dean, Prof Stefan Bornstein, has told Times Higher Education that plans for the new King's campus are already "in the process".
Prof Bornstein, who is director and chairman of TU Dresden's department of medicine and an honorary consultant in diabetes and endocrinology at King's, said the plan would allow King's to have a presence in Europe and maintain access to European research funding post-Brexit.
Likewise, he said, TU Dresden would benefit from increased ties to London, one of the "leading academic centres in the world".
Prof Bornstein said the new campus would hopefully run new undergraduate courses "linked to innovation and the needs of industry and society".
The aim would be to recruit leading scholars from around the world, he added.
Prof Bornstein said the Transcampus project had been envisaged before the EU referendum but admitted that it had become "a lot more interesting" since the vote.
"We cannot allow things that have developed for so many years in a positive way [to be] hampered by political decisions that actually nobody wanted," he said.
"It's a nice way to have a solution to get around this very stupid Brexit idea."
A number of UK universities are believed to be considering opening branch campuses in Europe after Brexit - though earlier this year Oxford University rejected reports that it was in talks to open a Paris campus.
Prof Bornstein said he would expect the Transcampus model to be replicated by other universities in the UK and Europe, but stressed that the key was a long history of collaboration between researchers at the two institutions.
In a statement, King's said the university valued the Transcampus initiative "which demonstrates the success of cross-national and institutional links".
"We will continue to work together in various fields on research and exchange and discuss potential further collaborations."
King's College London could become the first British university to open a European campus since the referendum.