Bethesda Research Laboratories, the Gaithersburg, Md.-based genetic engineering supply company, announced today that it was discussing a possible merger with the Dexter Corp.'s GIBCO division. The two companies announced that they would consider a public offering for the stock of the new company.

The Dexter Corp., of Windsor Locks, Conn., is a diversified manufacturer of specialty materials and the oldest company listed on the New York Stock Exchange. Its GIBCO division markets tissue-culture products and bacterial culture products for disease diagnosis. Dexter's Life Science group, of which GIBCO is the principal part, had net sales of $77 million in 1982.

BRL, which according to members of its board of directors was close to bankruptcy a little more than a year ago, produces a line of biotechnology research and clinical diagnostics products using recombinant DNA techniques. The company, founded in 1976, had revenues of $13 million in 1982.

"We have an opportunity to create one of the industry's largest higher-technology companies, capable of serving the scientific community by offering tools they need to conduct their research," said BRL Chairman Frederick R. Adler. Adler would assume the chairmanship of the new company, which has yet to be named.

Dexter plans to spin off the GIBCO division, merge it into BRL and turn it into a separate subsidiary of the parent company, BRL sources said. According to BRL, the new company would be expected to have annual sales approaching $100 million.

BRL, now privately held, was recently reorganized at the direction of Adler and other investors. By merging with GIBCO, BRL hopes to expand its array of products and its distribution network. By going public, it hopes to raise the capital to pay for further expansion.