Rep. Stanford E. Parris (R-Va.) held his fingers less than an inch apart yesterday and proclaimed that the federal government, Alexandria and private property owners are "that close" to reaching an agreement about the long-delayed development of the city's historic waterfront.

"I want a solution in my lifetime," Parris, 51, told a gathering of about 50 Northern Virginians in a small room in the Capitol, "and I do not have eternal life." He predicted accord would be reached no later than June 1.

"It will require a compromise" between developers and environmentalists, which the 8th District representative said will allow something "less than a Crystal City and more than a Belle Haven Country Club" to be built along the Potomac.

Parris said any solution should give complete control over development to the city, and not to the federal government, which has claimed ownership to some of the city's most valuable riverfront property in a lawsuit. The representative said he would prefer the agreement result in a court order, settling that dispute. But if that proves impossible, Parris said, he is prepared to introduce legislation to award control of the disputed acreage to the city.

Parris said he believes the federal government has "zero interest" in the area, and given the conservative bent of the Reagan administration, said it is "absolutely unreasonable to expect" that the U.S. will provide money to obtain clear title to four privately held riverfront properties.They are valued at about $46 million, he said.

Alexandria Vice Mayor Robert Calhoun added that he is "not convinced that it is prudent to expend public money" to put all of the 1.5 mile waterfront in downtown Alexandria under public ownership.

The Alexandria City Council has scheduled a public hearing on five alternatives to development of the waterfront area on May 10, and 30 days before that, interested parties will get copies of the proposals.