Coverage of the funeral of Soviet leader Konstantin Chernenko will start at 5 a.m. tomorrow morning on all three networks . . .

ABC anchor Peter Jennings will be in New York, with bureau chief Walter Rodgers in Moscow . . .

CBS coverage will begin live during its regular "Nightwatch" program . . .

NBC coverage will be anchored by John Palmer with Moscow bureau chief Steve Hurst and commentary by Steve Cohen of Princeton University . . .

Coverage may extend into the regular early morning programming on all three networks . . .

CBS special correspondent Walter Cronkite will speak on the future of the press and free specch at a private dinner tomorrow night given by the Congressional Clearing House on the Future, which is chaired by Rep. Robert Edgar (D-Pa.). Sen. John Heinz (R-Pa.) is vice chair of the caucus. . .

And on Friday, "Freedom of Information Day," retired general William Westmoreland, who recently withdrew his libel suit against CBS, will be guest speaker at a joint lunch of the National Press Club and the Society of Professional Journalists at the Press Club . . .

We understand that NBC Sports executives are courting -- you should pardon the expression -- the National Basketball Association, whose current $66 million contract with CBS will be up in the spring of 1986 . . .

And there's a chance that ABC Sports, which carried the NBA years ago, might be interested in renewing ties with the pro basketballers again, too . . .

The word in the industry is that ABC isn't all that excited about the prospect of carrying the U.S. Football League if and when it tackles the NFL head-on in the fall of 1986 and could be looking for a late fall 1986 replacement in its otherwise solid sports schedule (even in the springtime, the USFL plays in too many small TV markets to make it attractive to ABC's advertisers) . . .

But even if ABC doesn't get involved in the bidding, both NBC and the NBA have good reasons for a switch. The former is almost certain CBS won't relinquish its rights to the NCAA college basketball playoffs and without them, college hoop tilts don't draw enough during the regular season to make them worthwhile for NBC, which shares the regular-season games with CBS . . .

The NBA, on the other hand, is stymied by the tough contract the NCAA signed with CBS -- which doesn't allow promos for NBA games on CBS during the college playoffs, which start March 14 and wind up April 1 . . . just when the NBA wants to start generating excitement for its own upcoming playoffs . . .

CBS Sports is doing fairly well with the NBA this year, although ratings are down after a fast start. The key to increased interest in the NBA from all the networks is that CBS managed to cut the number of regular-season games, which don't draw too well, to just 11, while getting rights to broadcast up to 25 playoff games, including five in prime time, should the NBA championship series go to seven games. With the prospects of another finale involving a major TV market like Los Angeles, Boston or New York, the NBA looks attractive once again . . .

NBC Sports, in turn, is showing renewed interest in more conventional events, though it's had some success with its made-for-NBC "Breeders Cup" thoroughbred races and "Skins Game" golf matches . . .

NBC recently outbid CBS -- by a mere $1 million -- for the rights to NFL Monday night and playoff games on radio, after they'd been on CBS for seven seasons. Meanwhile, industry sources tell us that CBS Sports, on orders from the Very Top, is watching its budget . . .

Speaking of college hoop tilts, that Georgetown-St. John's Big East finale on Channel 5 Saturday night averaged an 18.0 Nielsen rating and a 32 percent audience share locally between 7 and 9:30. . . Wait, There's More

The board of the Telecommunications Research and Action Center (TRAC), the nation's oldest and largest media reform organization, has established the Donald H. McGannon Public Interest Telecommunications Award, to be given annually to an "individual or company in the industry that has made a unique and outstanding contribution to the advancement of women and minorities in the media" . . .

Joel Chaseman, president of Post-Newsweek Stations Inc., will be the first recipient of the award, which will be made at the Second Public Interest Telecommunications Celebration, to be held at the Waldorf-Astoria Hotel in New York, March 28 . . .

McGannon is the late president and chairman of Westinghouse Broadcasting . . . where Chaseman served as senior vice president, programming, and as president of the TV Group . . .

In announcing its choice, TRAC cited Chaseman's tenure at Post-Newsweek, during which, TRAC said, "he has demonstrated a deep commitment to assuring that women and minorities are employed and promoted. Currently, there is a woman or minority holding one of the top management jobs, including president and general manager of one station; news director; corporate general counsel; promotions manager and many other top positions at each Post-Newsweek station" . . .