Merger fever spread to the catalogue showroom industry yesterday when Best Products Inc. of Richmond, the industry's largest chain, announced plans to acquire the third largest, Modern Merchandising Inc., for stock worth an estimated $109 million.

If the agreement is approved by stockholders and regulators, Best will grow from 100 stores in 11 states to 172 stores in 26 states.

A chain with annual sales of more than $1.75 billion would be created by merging Best with Modern, which is based in Hopkins, Minn., a suburb of Minneapolis-St. Paul.

Best would also become the nation's largest publisher of catalogue showroom catalogues, because Modern Merchandising also puts out catalogues for other showroom operators, including Best.

Under the agreement, Modern Merchandising's shareholders would receive 0.73 share of Best common stock for each share of Modern.

Best shares closed Thursday at 17 1/8. Modern Merchandising last traded at 11 1/8. At Thursday's price, Best's offer for Modern Merchandising was worth about $12.50 a share.

Analysts said the offer seemed to be low, but noted that the acquisition would tend to dilute Best's earnings because the company would have to issue 6.3 million new shares.

The deal was announced late yesterday after trading on both stocks was halted Thursday.

Although the merger requires approval by the Federal Trade Commission, securities analysts said they didn't expect regulators to challenge it. Although the two companies are at the top of their industry, Best and Modern Merchandising do not compete directly in any geographic areas.

Best showrooms are primarily on the East Coast, Texas and California. Modern Merchandising runs similar catalogue stores under the names LaBelle's, Dolgins, Jafco, Miller's and Great Western, mostly in the Midwest and Northwest.

Best and Modern Merchandising have business ties that go back many years. The Best catalogue is published by Creative Catalogue Inc., a Modern subsidiary.

As the producer of Best's catalogue, Modern prints the books and makes many of the decisions about what merchandise is included in them.

Modern Merchandising Chairman Harold Roitenberg is expected to remain in his post.

Best already had announced plans to acquire the 19 Basco Inc. catalogue stores for $5.4 million. The deal is expected to be completed next month.

Modern Merchandising had sales of $715 million in the fiscal year ended Jan. 30 and posted a dramatic increase in earnings, from $1.3 million (10 cents a share) in 1980 to $5.45 million (64 cents).

First-quarter revenues at Modern Merchandising fell from $136.1 million last year to $123.5 million. Earnings for the period increased slightly, from $2.2 million (26 cents) last year to $2.3 million (27 cents) this year.

Best had sales of just over $1 billion in the fiscal year ended June 28, 1981, and earned $24 million ($2.49). The company then changed its fiscal year and, in the seven months ended Jan. 30, had sales of $772.7 million and profits of $19.5 million ($2.01).

In the first quarter of 1982, Best had sales of $215.8 million, but lost $3.2 million, primarily due to heavy advertising and the expense of opening eight new stores.