Exhibit 32

Certification of Chief Executive Officer and Chief Financial Officer

Pursuant to

18 U.S.C. Section 1350 as Adopted Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

In connection with the Annual Report on Form 10-K of Goldman Sachs Private Middle Market Credit LLC (the “Company”) for the quarter ended December 31, 2016 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), Brendan McGovern, as Chief Executive Officer of the Company, and Jonathan Lamm, as Chief Financial Officer of the Company, each hereby certifies, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to the best of his knowledge:

1. The Report fully complies with the requirements of Section 13(a) of the Securities Exchange Act of 1934, as amended; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: February 28, 2017

Date: February 28, 2017