Goldman Sachs Group Inc.’s infrastructure arm and Canadian pension fund Ontario Municipal Employees Retirement System are part of a group that is nearing a deal to buy a majority stake in Germany’s Amedes Holding GmbH, a provider of medical-diagnostic services including Covid-19 tests, according to people familiar with the matter.

The deal would value the business at close to $1.9 billion, including debt, the people familiar with the matter said. Goldman and Omers, plus AXA Investment Managers—the asset-management business of global insurer AXA SA—are buying the controlling stake from European buyout firm Antin Infrastructure Partners.

Based in Hamburg, Germany, privately held Amedes offers diagnostic services for patients, resident doctors and clinics at laboratories and practices in Germany and Belgium. Its business handles PCR tests that are used to diagnose Covid-19.

The acquisition would allow the buyers to take advantage of strong demand for PCR diagnostic services. However, that business could be at risk of slowing if the rollout of vaccines successfully combats the virus’s spread.

The fight against Covid-19 has highlighted the importance of healthcare services. It has also shown how the definition of infrastructure has expanded beyond such traditional assets as toll roads and pipelines to include businesses in busing, aviation services and healthcare. The ability to generate steady recurring revenue is a common link between them.

A deal, if completed, could be announced later Friday, people said. It would be done at a valuation of close to 1.6 billion euros, the people said, equivalent to around $1.9 billion.

Reuters previously reported that Omers was nearing a deal, but the other members of the consortium and the valuation hadn’t been disclosed.

Antin, which has headquarters in Paris, London and New York, acquired a majority stake in Amedes in 2015 from General Atlantic, a U.S.-based growth investor. Since then, the business has expanded its laboratory network from about 62 laboratories and practices to more than 70.

Focused on infrastructure assets in Europe and North America, Antin targets deals in the energy and environment, telecommunications, transportation and social sectors.

Write to Ben Dummett at ben.dummett@wsj.com