Asked by journalists on the sidelines of the EU summit in Salzburg whether he would put himself forward as a candidate to take over from Juncker, Kern replied: "Yes, that is correct. I am available.
"There are other candidates, too, that's clear. But we'll find the very best candidate."
Kern, 52, became chancellor in 2016, but lost in a snap election to conservative Sebastian Kurz just a year later.
Kern was attending the EU summit in Salzburg to drum up support for his candidacy ahead of a meeting in Lisbon in December where the Social Democrat (S&D) grouping will choose its contenders.
Earlier this week, Commission vice president Maros Sefcovic, a 52-year-old Slovakian national, announced his candidacy for the S&D grouping.
"We have to restore Social Democracy here in Europe. We have a lot of issues and challenges. We have to define a strategy, we have to define the issues, we have to define the campaign to request one of the leading positions
in Europe," he said.
Juncker is scheduled to leave office at the end of October 2019 after a term marked by a series of crises, including a huge influx of refugees, soaring debt and Brexit.
His successor will be chosen by a so-called "Spitzenkandidat" procedure, a term meaning "lead candidate" in German, which was used was for the first time to appoint Juncker in 2014.
Under the system, the largest party in the European Parliament after elections nominates its candidate for the post.
The next European parliamentary elections are being held in May 2019.
The S&D is currently the second biggest group in the European Parliament after the right and centre-right PPE from whose ranks Juncker came.
German MEP Manfred Weber has already announced his candidacy for the PPE grouping.