J. William Middendorf II -- composer, runner, art wheeler-dealer, financier, secretary of the Navy for President Ford, campaigner and CIA transition team leader for President-elect Ronald Reagan -- dearly wants to be secretary of defense.

Forget that he has done a few offbeat things in the past, like dancing in a bear suit at a birthday party while Navy secretary. This guy really knows defense, his champions are claiming in their telephone calls. Middendorf has made lots of calls of his own in pursuit of the Pentagon's top job, though friends say he would have settled for second spot to Sen. John Tower (R-Tex.), had Reagan tapped Tower for the Pentagon's number one.

But, with Tower's chances apparently fading, Middendorf and his allies are out for defense's top job. What galls Middendorf's horse-holders is the possibility that Casper W. Weinberger -- Nixon's director of the Office of Management and Budget and a top Reagan economic adviser -- might unhorse Middendorf and become secretary of defense himself.

Weinberger said over the weekend that Reagan has not asked him to be defense secretary, seemingly leaving the door open for an invitation.

Middendorf fans say Weinberger definitely would not fit at defense. Said one: "Cap the Knife was the guy cutting the defense budget while Middendorf was trying to raise it."