Alexandria hopes to get $1.1 million in federal and state funds next year as part of a major park and recreation improvement program that would expand the city's bike trail system and upgrade several city parks.

Among other Northern Virginia localities, Arlington has requested no conservation funds so far, but Fairfax County expects to request nearly $500,000 to help it acquire a 12-acre park beside the new Huntington Metro station, just south of Alexandria and the Beltway.

Alexandria has asked for $450,000 from the federal Land and Water Conservation Fund to improve Chinquapin Park, adding tennis and handball courts and a larger community garden. The funds also would provide trails at Dora Kelley Nature Park and would add several miles of bike trails from Chinquapin along Taylor Run to Duke Street, along Cameron Valley and in an abandoned two-block-long railroad tunnel in Old Town. The city also hopes to get a $75,000 state grant, which the city must match with $25,000, to help with the bike trail addition.

A decision on the $450,000 request is expected today at a meeting of the Virginia Commission of Outdoor Recreation, which oversees allocation of $4.7 million the state expects to receive from the conservation fund. If the grant is approved, the city must provide $450,000 in matching funds.

The city also hopes to get another grant of $572,000 from the federal Urban Park and Recreation Recovery Program to rehabilitate and expand the Cameron Valley recreation center. The center is part of a city public housing project near Duke Street and east of Quaker Lane.

The grant, designed to help restore the nation's urban parks, hinges on approval of a 15 percent matching state grant, which the Commission of Outdoor Recreation also is expected to decide today.

At Chinquapin Park, five outdoor tennis courts and one handball court would be built with the Land and Water Conservation Fund money, the community garden expanded from 75 to 145 plots and water extended to the site, playgrounds built at the park and at nearby Angel Park and a bike and nature trail built along Taylor Run, the creek that runs from the park along Hammond and Taylor Run Parkways to Duke Street.

The city is now building major sections of its bike trail system with the last of more than $450,000 in Land and Water Conservation Fund grants, under eight-lane Shirley Highway along Holmes Run and along Cameron Valley parallel to the Beltway. The new grant would extend the trail under Telegraph Road to Rte. 1 and also pave the Old Town railroad tunnel along Wilkes Street.

In a separate action, the city approved the hiring of a consultant to study how to spend the $2.1 million approved in last summer's bond issue for a community center and indoor swimming pool at Chinquapin. The complex at the city's largest park would replace the existing World War II "tempo" building and community center. Construction could start by the end of 1981 and be finished within a year, according to city officials.