The Kresge Foundation will grant $500,000 to the Fogg Art Museum, contingent upon the Fogg's success in raising the rest of the money needed to build a two-story addition to the museum, sources in the Development Office said this week.

The Fogg, through the Development Office, must raise $2.8 million by July 15, 1978 to qualify for the grant, but fundraisers said yesterday they are optimistic about their chances of success.

The Fogg has already raised $4.1 million, including the Kresge grant, toward its current fundraising campaign goal of $15.7 million. Although some of that money is restricted for specific purposes, the amount may already include enough unrestricted money to match the Kresge grant, Karen D. Hunzicker-Putnam, a development officer working on the Fogg drive, said.

In addition to building a new wing, Fogg officials said they hope to renovate existing gallery and study facilities and install a climate control system to regulate the 50-year-old building's temperature and humidity.

"The Kresge Foundation is one of the few that concentrates on [funding construction of] facilities. I'm pleased that they were willing to do this for the Fogg," Alfred M. Gibbons, director of the Development Office, said yesterday.

Suzannah Doeringer, assistant director of the Fogg, said yesterday the Kresge gift will add impetus to the drive when it "goes public" in October.