The Arlington County Board yesterday directed County Manager W. Vernon Ford to begin intensive negotiations with owners of Parkington, Northern Virginia's oldest shopping mall, an action regarded as crucial to the planned redevelopment around a recently opened Metro station.

Last fall the St. Louis-based May Department Stores Co., owners of the mall, and the Taubman Corp., a Michigan-based developer, told the county they wanted the county to back their plans to remodel the 27-year-old shopping center.

Officials of the May Co., which owns the 14-acre mall located at the intersection of Wilson Boulevard and N. Glebe Road, have called the area "super viable" because of its proximity to Metro. The May Co. also owns Hecht's, one of two major stores in the mall.

When redevelopment plans were unveiled, May officials said they were willing to spend $100 million to transform the unenclosed pea-green mall from its somewhat shabby condition to a two-story structure containing 30 boutiques, but only if the county was willing to contribute about $13 million toward the redevelopment. Preliminary plans call for the demolition of the one-story mall except for the Hecht's building and relocation fo the J.C. Penny store.

Company officials suggested that Arlington's contribution should be construction of a three-level parking garage underneath the two-story mall. The cities of Stamford, Conn., and White Plains, N.Y., have made similar contributions, according to Taubman executives.

Some Arlington officals have balked at such a contribution, which is likely to be a major point in the coming negotiations that are expected to last nine months. Redevelopment is not expected to occur before 1982.

Several residents yesterday also expressed reservations about making any financial contribution to the project. "I don't think this should be an Arlington Chrysler project," said one man, referring to the federal government's bailout of the financially beleaguered auto maker. "If May Company is not that interested inn putting their own money into this, then someone else will."

County Board Chairman Walter L. Frankland Jr. said that hiring an experienced negotiator was vital if the county is to secure the most favorable deal possible for a redevelopment effort that would "significantly improve the county's tax base," and help pay for Metro.