Let the David Letterman sweepstakes begin … officially.Last week NBC and the disgruntled latenight host agreed to a compromise that would allow Letterman to talk with other interested parties; in exchange, Letterman extended his role as host of “Late Night With David Letterman” by at least a couple of extra months, through the 1993 May sweeps. Although some sources indicate that Letterman is “all but gone” and virtually certain to sign with another network or syndicator, NBC wasn’t prepared to make that concession, saying in a statement, “NBCreiterates its desire to continue its longstanding relationship with David Letterman and remains hopeful that it will extend his contract beyond next June.” Network officials also were privately indicating that they felt they still had a shot at keeping the hard-to-read Letterman, whose reported suitors including ABC, CBS, Fox Broadcasting Co., Fox’s syndication wing Twentieth TV, Columbia Pictures TV Distribution and King World. Letterman’s existing contract would have expired in early April and barred him from entering into talks with other parties until that point. He has already retained Michael Ovitz of Creative Artists Agency to handle his contract dealings and has reportedly met informally with several interested parties. Tellingly, any comment from the Letterman camp was referred to CAA, which said it wouldn’t discuss the status of negotiations. In NBC’s statement Letterman noted that the announcement “does not represent a final decision” regarding his future at the web. Aside from extracting an assurance that Letterman would stay through the sweeps, NBC, by freeing him to negotiate officially with outside parties, also may be looking toward the future–realizing that it will need time to ready a replacement if Letterman does opt to depart. NBC has signed “Saturday Night Live’s” Dana Carvey to a wide-ranging exclusive deal and, according to published reports, might try to craft a show around him if Letterman exits. Carvey recently agreed to continue appearing on “SNL” through the rest of the current season. Letterman has frequently been the subject of rumors that he would leave during his 10-year NBC tenure, but the speculation has been almost constant since NBC selected Jay Leno instead of Letterman as the heir to Johnny Carson on “The Tonight Show.” Letterman was reportedly miffed that he wasn’t notified in advance and also took umbrage over NBC licensing repeats of “Late Night” to the Arts & Entertainment network without consulting him. Fox is already securing clearances for its own new latenight talk show next fall starring Chevy Chase but is said to still be interested in Letterman. ABC, which has repeatedly denied its interest, would like the host to follow “Nightline,” while CBS would apparently give him the 11:30 p.m. berth he wanted at NBC, opposite Leno. Latenight is a valuable daypart in terms of sales and Letterman has a loyal following in key younger demographics, although it’s yet to be established whether he could broaden that core audience if moved to an earlier slot.