UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 6-K

REPORT OF FOREIGN PRIVATE ISSUER PURSUANT TO RULE 13a-16 OR

15d-16 UNDER THE SECURITIES EXCHANGE ACT OF 1934

For the month of October 2026

Commission File Number 001-33060

DANAOS CORPORATION

(Translation of registrant’s name into English)

Danaos Corporation

c/o Danaos Shipping Co. Ltd.

14 Akti Kondyli

185 45 Piraeus

Greece

Attention: Secretary

011 030 210 419 6480

(Address of principal executive office)

Indicate by check mark whether the registrant files or will file annual reports under cover of Form 20-F or Form 40-F.

Form 20-F x          Form 40-F ¨

INFORMATION CONTAINED IN THIS FORM 6-K REPORT

Danaos Corporation (“Danaos” or the “Company”) is exploring a carve-out and sale of a minority stake in its dry bulk segment, and has mandated investment banking firms to advise on this potential equity placement and listing in the Norwegian market. This is being undertaken as part of the Company’s broader strategy focused on value creation and shareholder returns.

The Company’s dry bulk business, for which Danaos Bulk Inc. acts as the holding company, currently comprises 11 Capesize vessels on-the-water and four Newcastlemaxes under construction scheduled to be delivered in 2028.

There can be no assurance that any transaction or listing will be pursued or completed, or as to its terms or timing.

This announcement does not constitute an offer to sell or the solicitation of an offer to buy any securities. The securities referred to herein have not been and will not be registered under the U.S. Securities Act of 1933, as amended, and may not be offered or sold in the United States or to U.S. persons absent registration or an applicable exemption from registration requirements.

*****

This report on Form 6-K is hereby incorporated by reference into the Company’s (i)  Registration Statement on Form F-3 (Reg. No. 333-237284) filed with the SEC on March 19, 2020, (ii) the post-effective Amendment to Form F-1 in the Registration Statement on Form F-3 (Reg. No. 333-226096) filed with the SEC on March 6, 2019, (iii) Registration Statement on Form F-3 (Reg. No. 333-174494) filed with the SEC on May 25, 2011, (iv) Registration Statement on Form F-3 (Reg. No. 333-147099), the related prospectus supplements filed with the SEC on December 17, 2007, January 16, 2009 and March 27, 2009, (v) Registration Statement on Form S-8 (Reg. No. 333-233128) filed with the SEC on August 8, 2019 and the reoffer prospectus, dated August 8, 2019, contained therein, (vi) Registration Statement on Form S-8 (Reg. No. 333-138449) filed with the SEC on November 6, 2006 and the reoffer prospectus, dated November 6, 2006, contained therein, (vii) Registration Statement on Form F-3 (Reg. No. 333-169101) filed with the SEC on October 8, 2010, (viii) Registration Statement on Form F-3 (Reg. No. 333-255984) filed with the SEC on May 10, 2021 and (ix) Registration Statement on Form F-3 (Reg. No. 333-293934) filed with the SEC on March 2, 2026.

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Date: October 9, 2026