The concordat is being developed by Universities UK and research funders, and a draft was published in April. It sets out the standards required of researchers, funders and universities, but makes clear that primary responsibility for policing misconduct rests with institutions.
A paper prepared for Hefce's board meeting on 30 April and published late last month invited the board to approve a plan, subject to consultation, to introduce compliance with the concordat as part of the financial memorandum universities sign with Hefce.
A Hefce spokesman said the plan was subject to confirmation once the final version of the document, expected in July, was published.
The paper says the move would "provide assurance to the government and the...public that public funding for research is used with integrity and that appropriate mechanisms are in place to identify and respond to...misconduct".
It adds that Hefce understands that "the other major UK funders" are also considering making compliance a condition of their grants.
Chris Hale, deputy director of policy at Universities UK and one of the concordat's authors, welcomed Hefce's proposal and pointed out that the concordat had been modelled on the research integrity requirements already included in research council grant agreements.
The concordat represents funders' preferred approach to research integrity after funding for advisory body the UK Research Integrity Office ended in 2010.
Daniele Fanelli, a Leverhulme early career fellow at the University of Edinburgh and an expert in the field, said the concordat's emphasis on the role of institutions was an improvement on the "tendency" to hold only individuals accountable. But this was only one aspect of a solution that should also include "rethinking criteria for career advancement, public funding, education and publications".